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Logic Homework Help

Quality Score: 9.8 /10 from 7,285 customers

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Benefits you get when you order help with logic homework

If you’re looking for someone reliable to ask, “do my logic homework for me,” you’re in the right place. We’ve created and perfected a system that gives you multiple opportunities while ensuring your safety and the correctness of all solutions delivered. Here are some facts that prove that those aren’t just pretty words.

We can solve problems of any difficulty

Whether you’re struggling with model theory or can't wrap your mind around recursion, we’re there to offer assistance. All you need to do is say, “please give me help with logic homework,” and we’ll find an experienced specialist who understands what you need and how it has to look. This expert will do their best to comply with your deadline, and we’ll do everything possible so that your experience remains stress-free.

You can get hands-on skills by relying on us

Mathematical logic is more than just a tough subject. In fact, you can boost your cognitive abilities and better prepare for life if you do your logic homework with a full understanding of all your assignments. The examples from our experts will certainly help you get to the point faster and solve everything with minimal effort. As you can see, our assistance is always result-oriented.

Manage your time with maximum efficiency

Getting help with logic homework is always a smart decision, because this choice allows you to plan your leisure time more effectively. Every hour you would spend googling examples that just don’t meet your expectations will surely find a better use if you receive such samples directly from trustworthy mathematicians. That’s why it makes sense to order the solutions you require in advance.

Excel in the classroom every time

The fact is, all students want and need to get as many points as possible. We understand that you hope to improve your academic performance when you ask, “do my logic homework online.” Correspondingly, we design our help so that you can learn and solve all similar problems in the future, getting ready for any tests, no matter how hard they may be.

Get all the help you need!

If you struggle with Logic Homework, don’t get desperate. Just ask our experts for help, and use our solutions to understand your Logic Homework better!

Student Reviews

I googled “ homework help logic ” and this was one of the first results. I was skeptical at first, but now I’m really happy I tried this service because my solution is thorough and correct. I can certainly recommend this site to anyone who’s having trouble with that discipline.

Christian Jones

So, I wanted to pay someone to do my logic homework , and it turns out, I chose the right company! They do everything faster than expected, they care about the opinion of every customer, and their support operators do their job well. If there’s another topic I can’t cope with, I’ll come here again.

I asked one of the experts to do my logic homework and received the finished assignment before the deadline! I was impressed by the level of attention and care because my specialist asked me about some details to make everything look exactly like I wanted it to. I’ll definitely use this site again.

Thomasina O’Brien

I was really desperate for help with infinitary problems, and was ready to scream, “ do my logic homework for me, please! ” Then my friend recommended this site, and I was blown away by how well it worked. Sure, sometimes you need to wait a little before you get an answer from their support team, but everything is correct, so that’s a minor inconvenience!

Sarah Berrie

How long does it take you to help me with my logic homework?

This depends on the size and difficulty of your task. If you need the solution urgently, our experts will do everything in their power to meet that request and get you what you need. 24 hours will probably be the most realistic time frame for most assignments. Still, it’s important to remember that shorter deadlines cost more than longer ones, so ordering in advance can save you some money. Furthermore, it’s always nice to have some extra time for corrections if they are necessary. Smart planning is essential.

Is it ethical to use your service?

Yes, it’s 100% ethical and secure. We treat everyone who comes asking, “do my logic homework for me,” with respect, so our service abides by all the regulations and laws for this kind of assistance. What's more, we make sure to protect your data, such as phone numbers and email addresses. We share that information with nobody, only using it to send you the ready task or consult you about some details. Therefore, you can rest assured that you’re doing the right thing by addressing your academic needs and getting a sample that teaches you to study logic efficiently.

What kind of education do your experts have?

Each expert must get at least a college degree before applying for the job. In addition, every specialist who provides students with logic homework help on our behalf has passed several tests ensuring that they have all the necessary knowledge and skills. That way, we can guarantee that they also know how to manage their time and pay attention to every detail of an assignment. We never tolerate incorrect solutions or a lack of discipline. That’s why we can state with confidence that we’ll match your order with the best available expert who can complete it at the highest level.

Want to pay someone to do your Logic Homework? Our experts are ready to provide you with custom solutions and help you do your task in a heartbeat!   Domymathhomeworks.com

Who can do my logic homework for me fast?

The life of many students is far from easy, with part-time jobs and sleepless nights, not to mention countless family errands. Such a schedule could drive anyone crazy, so it’s no wonder that many youngsters just don’t have many opportunities to spend hours trying to comprehend mathematical logic.

That’s why services like ours have appeared, trying to make your life easier by offering something we can do really fast and well. Many of our experts have been in similar situations themselves, so now they happily answer any struggling learner who searches for someone to “do my homework logic.”

The experience of our specialists allows them to complete almost any task with nearly lightning speed. They are proficient in all formal logic systems, and first-order logic is like a game to them. These experts do their part from across the globe, so our service can work around the clock, tackling orders as soon as they come in.

We focus on precision and quality, trying to get it right every time. Moreover, as many customers mention in their reviews, we often deliver the ready-made assignment before the deadline, just to be on the safe side. If this approach suits you, you’ll like the results we can offer.

Like any respectable company, we have several guarantees that ensure your satisfaction and include contingencies for even the worst-case scenarios. For instance, let’s imagine you’ve ordered logic homework help, but there’s something that doesn’t match the instructions and needs fixing. In that case, you can request a free revision, and it will be done as soon as possible.

The human factor is always there, and the best we can do is to correct anything that goes wrong. Moreover, we’ve got a customer-friendly money-back guarantee that secures your finances. In other words, you’ll be refunded a fair amount if we fail to meet your expectations.

The main advantages of our service

When people ask us, “do my logic assignment right now,” they hope for the best results. Let’s look at the facts that explain why meeting your expectations is our everyday reality.

• A quality score of 9.8/10 . That’s pretty close to perfection, and we constantly do everything we can to keep up the good work. However, even such a high rating would be worth a lot less if it came from a single critic. Instead, it’s the ranking that 7,285 customers have given us, so it’s really representative.
• Affordable prices. We realize that the people who ask us, “do my logic homework,” are looking for reasonable options, not sky-high pricing. Hence, we make our work as accessible as possible, trying to keep the rewards for the experts fair. As the reviews show, we’ve managed to maintain that balance so far.
• Direct communication with your expert. It might happen that you accidentally forget about some important remark or additional request that can influence the entire solution. We understand how vital details are in logic, so we’ve created a system where you can notify the specialist about your wishes via direct message. There’s nothing complicated about it, and timely communication can minimize corrections and make the results pleasant on the first try.
• 385 proficient experts . All of them are qualified and have experience in helping learners. Therefore, you can rely on any specialist, knowing that they’ll meet every requirement you set. Working 24/7, many of them have perfected their skills to the highest achievable level, so there’s virtually nothing impossible for these mathematicians. Many of them particularly enjoy logic, so you can order the required task and relax until the sample arrives.
• More than 122 completed orders daily . This number demonstrates that our service is really necessary for many students in multiple countries. The internet has taken our speed to the next level, and now we can solve problems and deliver them in a matter of hours. All you have to do is leave a corresponding request and pay for the assignment.

How to use logic homework help to its full potential

As you can see, logic homework help is indispensable for many learners. It’s an opportunity to study better, use your time more efficiently, and enjoy life without sleepless nights. Still, there are a few tips that can help you get the most out of the sample you receive from our expert. Let’s analyze the study process and see what they are.

Check the solution for errors . People are naturally prone to make mistakes, so you should ensure that everything’s right before jumping to the desk and beginning to study. Use your textbook and lecture notes to verify the accuracy of the completed task you receive. If something is wrong, you can ask for a revision. If everything is correct, proceed to the next step.

Understand how your expert did it . When you ask, “do my logic task,” you know in advance that whoever is going to help you will put a lot of thought into the solution. The same goes for you as a learner, because you have to see how all the components work together before tackling similar assignments. Don’t neglect this chance to cement your new skill once and for all. Do you need help with logic homework? Get assistance and try to practice.

Try to solve other problems with the mechanisms you’ve learned. Remember that practice makes perfect. It’s an old saying, but it works every time, so it’s better to spend half an hour honing your new skill than to forget it almost instantly.

Of course, these methods don’t work for every single individual. If you have other approaches that suit you more than they do anyone else, just follow them and trust yourself.

Choose Your Test

Sat / act prep online guides and tips, the 5 best homework help websites (free and paid).

Other High School , General Education

Listen: we know homework isn’t fun, but it is a good way to reinforce the ideas and concepts you’ve learned in class. But what if you’re really struggling with your homework assignments?

If you’ve looked online for a little extra help with your take-home assignments, you’ve probably stumbled across websites claiming to provide the homework help and answers students need to succeed . But can homework help sites really make a difference? And if so, which are the best homework help websites you can use? 

Below, we answer these questions and more about homework help websites–free and paid. We’ll go over: 

• The basics of homework help websites
• The cost of homework help websites 
• The five best homework websites out there 
• The pros and cons of using these websites for homework help 
• The line between “learning” and “cheating” when using online homework help 
• Tips for getting the most out of a homework help website

So let’s get started! 

The Basics About Homework Help Websites–Free and Paid

Homework help websites are designed to help you complete your homework assignments, plain and simple. 

What Makes a Homework Help Site Worth Using

Most of the best sites allow users to ask questions and then provide an answer (or multiple possible answers) and explanation in seconds. In some instances, you can even send a photo of a particular assignment or problem instead of typing the whole thing out! 

Homework help sites also offer more than just help answering homework questions. Common services provided are Q&A with experts, educational videos, lectures, practice tests and quizzes, learning modules, math solving tools, and proofreading help. Homework help sites can also provide textbook solutions (i.e. answers to problems in tons of different textbooks your school might be using), one-on-one tutoring, and peer-to-peer platforms that allow you to discuss subjects you’re learning about with your fellow students. 

And best of all, nearly all of them offer their services 24/7, including tutoring! 

What You Should Should Look Out For

When it comes to homework help, there are lots–and we mean lots –of scam sites out there willing to prey on desperate students. Before you sign up for any service, make sure you read reviews to ensure you’re working with a legitimate company. 

A word to the wise: the more a company advertises help that veers into the territory of cheating, the more likely it is to be a scam. The best homework help websites are going to help you learn the concepts you’ll need to successfully complete your homework on your own. (We’ll go over the difference between “homework help” and “cheating” a little later!) 

You don't need a golden piggy bank to use homework help websites. Some provide low or no cost help for students like you!

How Expensive Are the Best Homework Help Websites?

First of all, just because a homework help site costs money doesn’t mean it’s a good service. Likewise, just because a homework help website is free doesn’t mean the help isn’t high quality. To find the best websites, you have to take a close look at the quality and types of information they provide! 

When it comes to paid homework help services, the prices vary pretty widely depending on the amount of services you want to subscribe to. Subscriptions can cost anywhere from $2 to $150 dollars per month, with the most expensive services offering several hours of one-on-one tutoring with a subject expert per month.

The 5 Best Homework Help Websites 

So, what is the best homework help website you can use? The answer is that it depends on what you need help with. 

The best homework help websites are the ones that are reliable and help you learn the material. They don’t just provide answers to homework questions–they actually help you learn the material. 

That’s why we’ve broken down our favorite websites into categories based on who they’re best for . For instance, the best website for people struggling with math might not work for someone who needs a little extra help with science, and vice versa. 

Keep reading to find the best homework help website for you! 

Best Free Homework Help Site: Khan Academy

• Price: Free!
• Best for: Practicing tough material 

Not only is Khan Academy free, but it’s full of information and can be personalized to suit your needs. When you set up your account , you choose which courses you need to study, and Khan Academy sets up a personal dashboard of instructional videos, practice exercises, and quizzes –with both correct and incorrect answer explanations–so you can learn at your own pace. 

As an added bonus, it covers more course topics than many other homework help sites, including several AP classes.

Runner Up: Brainly.com offers a free service that allows you to type in questions and get answers and explanations from experts. The downside is that you’re limited to two answers per question and have to watch ads. 

Best Paid Homework Help Site: Chegg

• Price: $14.95 to $19.95 per month
• Best for: 24/7 homework assistance  

This service has three main parts . The first is Chegg Study, which includes textbook solutions, Q&A with subject experts, flashcards, video explanations, a math solver, and writing help. The resources are thorough, and reviewers state that Chegg answers homework questions quickly and accurately no matter when you submit them.  

Chegg also offers textbook rentals for students who need access to textbooks outside of their classroom. Finally, Chegg offers Internship and Career Advice for students who are preparing to graduate and may need a little extra help with the transition out of high school. 

Another great feature Chegg provides is a selection of free articles geared towards helping with general life skills, like coping with stress and saving money. Chegg’s learning modules are comprehensive, and they feature solutions to the problems in tons of different textbooks in a wide variety of subjects. 

Runner Up: Bartleby offers basically the same services as Chegg for $14.99 per month. The reason it didn’t rank as the best is based on customer reviews that say user questions aren’t answered quite as quickly on this site as on Chegg. Otherwise, this is also a solid choice!

Best Site for Math Homework Help: Photomath

• Price: Free (or $59.99 per year for premium services) 
• Best for: Explaining solutions to math problems

This site allows you to t ake a picture of a math problem, and instantly pulls up a step-by-step solution, as well as a detailed explanation of the concept. Photomath also includes animated videos that break down mathematical concepts to help you better understand and remember them. 

The basic service is free, but for an additional fee you can get extra study tools and learn additional strategies for solving common math problems.

Runner Up: KhanAcademy offers in-depth tutorials that cover complex math topics for free, but you won’t get the same tailored help (and answers!) that Photomath offers. 

Best Site for English Homework Help: Princeton Review Academic Tutoring

• Price: $40 to $153 per month, depending on how many hours of tutoring you want 
• Best for: Comprehensive and personalized reading and writing help 

While sites like Grammarly and Sparknotes help you by either proofreading what you write via an algorithm or providing book summaries, Princeton Review’s tutors provide in-depth help with vocabulary, literature, essay writing and development, proofreading, and reading comprehension. And unlike other services, you’ll have the chance to work with a real person to get help. 

The best part is that you can get on-demand English (and ESL) tutoring from experts 24/7. That means you can get help whenever you need it, even if you’re pulling an all-nighter! 

This is by far the most expensive homework site on this list, so you’ll need to really think about what you need out of a homework help website before you commit. One added benefit is that the subscription covers over 80 other subjects, including AP classes, which can make it a good value if you need lots of help!  

Best Site for STEM Homework Help: Studypool

• Best for: Science homework help
• Price: Varies; you’ll pay for each question you submit

When it comes to science homework help, there aren’t a ton of great resources out there. The best of the bunch is Studypool, and while it has great reviews, there are some downsides as well. 

Let’s start with the good stuff. Studypool offers an interesting twist on the homework help formula. After you create a free account, you can submit your homework help questions, and tutors will submit bids to answer your questions. You’ll be able to select the tutor–and price point–that works for you, then you’ll pay to have your homework question answered. You can also pay a small fee to access notes, lectures, and other documents that top tutors have uploaded. 

The downside to Studypool is that the pricing is not transparent . There’s no way to plan for how much your homework help will cost, especially if you have lots of questions! Additionally, it’s not clear how tutors are selected, so you’ll need to be cautious when you choose who you’d like to answer your homework questions.  

What Are the Pros and Cons of Using Homework Help Sites?

Homework help websites can be a great resource if you’re struggling in a subject, or even if you just want to make sure that you’re really learning and understanding topics and ideas that you’re interested in. But, there are some possible drawbacks if you don’t use these sites responsibly. 

We’ll go over the good–and the not-so-good–aspects of getting online homework help below. 

3 Pros of Using Homework Help Websites 

First, let’s take a look at the benefits. 

#1: Better Grades Beyond Homework

This is a big one! Getting outside help with your studies can improve your understanding of concepts that you’re learning, which translates into better grades when you take tests or write essays. 

Remember: homework is designed to help reinforce the concepts you learned in class. If you just get easy answers without learning the material behind the problems, you may not have the tools you need to be successful on your class exams…or even standardized tests you’ll need to take for college. 

#2: Convenience

One of the main reasons that online homework help is appealing is because it’s flexible and convenient. You don’t have to go to a specific tutoring center while they’re open or stay after school to speak with your teacher. Instead, you can access helpful resources wherever you can access the internet, whenever you need them.

This is especially true if you tend to study at off hours because of your extracurriculars, work schedule, or family obligations. Sites that offer 24/7 tutoring can give you the extra help you need if you can’t access the free resources that are available at your school. 

#3: Variety

Not everyone learns the same way. Maybe you’re more of a visual learner, but your teacher mostly does lectures. Or maybe you learn best by listening and taking notes, but you’re expected to learn something just from reading the textbook . 

One of the best things about online homework help is that it comes in a variety of forms. The best homework help sites offer resources for all types of learners, including videos, practice activities, and even one-on-one discussions with real-life experts. 

This variety can also be a good thing if you just don’t really resonate with the way a concept is being explained (looking at you, math textbooks!).

Not so fast. There are cons to homework help websites, too. Get to know them below!

3 Cons of Using Homework Help Websites 

Now, let’s take a look at the drawbacks of online homework help. 

#1: Unreliable Info

This can be a real problem. In addition to all the really good homework help sites, there are a whole lot of disreputable or unreliable sites out there. The fact of the matter is that some homework help sites don’t necessarily hire people who are experts in the subjects they’re talking about. In those cases, you may not be getting the accurate, up-to-date, and thorough information you need.

Additionally, even the great sites may not be able to answer all of your homework questions. This is especially true if the site uses an algorithm or chatbot to help students…or if you’re enrolled in an advanced or college-level course. In these cases, working with your teacher or school-provided tutors are probably your best option. 

#2: No Clarification

This depends on the service you use, of course. But the majority of them provide free or low-cost help through pre-recorded videos. Watching videos or reading info online can definitely help you with your homework… but you can’t ask questions or get immediate feedback if you need it .

#3: Potential For Scamming 

Like we mentioned earlier, there are a lot of homework help websites out there, and lots of them are scams. The review comments we read covered everything from outdated or wrong information, to misleading claims about the help provided, to not allowing people to cancel their service after signing up. 

No matter which site you choose to use, make sure you research and read reviews before you sign up–especially if it’s a paid service! 

When Does “Help” Become “Cheating”?

Admittedly, whether using homework help websites constitutes cheating is a bit of a grey area. For instance, is it “help” when a friend reads your essay for history class and corrects your grammar, or is it “cheating”? The truth is, not everyone agrees on when “help” crosses the line into “cheating .” When in doubt, it can be a good idea to check with your teacher to see what they think about a particular type of help you want to get. 

That said, a general rule of thumb to keep in mind is to make sure that the assignment you turn in for credit is authentically yours . It needs to demonstrate your own thoughts and your own current abilities. Remember: the point of every homework assignment is to 1) help you learn something, and 2) show what you’ve learned. 

So if a service answers questions or writes essays for you, there’s a good chance using it constitutes cheating. 

Here’s an example that might help clarify the difference for you. Brainstorming essay ideas with others or looking online for inspiration is “help” as long as you write the essay yourself. Having someone read it and give you feedback about what you need to change is also help, provided you’re the one that makes the changes later. 

But copying all or part of an essay you find online or having someone write (or rewrite) the whole thing for you would be “cheating.” The same is true for other subjects. Ultimately, if you’re not generating your own work or your own answers, it’s probably cheating.

5 Tips for Finding the Best Homework Help Websites for You

Now that you know some of our favorite homework help websites, free and paid, you can start doing some additional research on your own to decide which services might work best for you! Here are some top tips for choosing a homework help website. 

Tip 1: Decide How You Learn Best 

Before you decide which site or sites you’re going to use for homework help, y ou should figure out what kind of learning style works for you the most. Are you a visual learner? Then choose a site that uses lots of videos to help explain concepts. If you know you learn best by actually doing tasks, choose a site that provides lots of practice exercises.

Tip 2: Determine Which Subjects You Need Help With

Just because a homework help site is good overall doesn’t mean that it’s equally good for every subject. If you only need help in math, choose a site that specializes in that area. But if history is where you’re struggling, a site that specializes in math won’t be much help. So make sure to choose a site that you know provides high-quality help in the areas you need it most. 

Tip 3: Decide How Much One-On-One Help You Need 

This is really about cost-effectiveness. If you learn well on your own by reading and watching videos, a free site like Khan Academy is a good choice. But if you need actual tutoring, or to be able to ask questions and get personalized answers from experts, a paid site that provides that kind of service may be a better option.

Tip 4: Set a Budget

If you decide you want to go with a paid homework help website, set a budget first . The prices for sites vary wildly, and the cost to use them can add up quick. 

Tip 5: Read the Reviews

Finally, it’s always a good idea to read actual reviews written by the people using these homework sites. You’ll learn the good, the bad, and the ugly of what the users’ experiences have been. This is especially true if you intend to subscribe to a paid service. You’ll want to make sure that users think it’s worth the price overall!

What’s Next?

If you want to get good grades on your homework, it’s a good idea to learn how to tackle it strategically. Our expert tips will help you get the most out of each assignment…and boost your grades in the process.

Doing well on homework assignments is just one part of getting good grades. We’ll teach you everything you need to know about getting great grades in high school in this article.

Of course, test grades can make or break your GPA, too. Here are 17 expert tips that’ll help you get the most out of your study prep before you take an exam.

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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• Number Theory
• Probability
• Everyday Math
• Classical Mechanics
• Electricity and Magnetism
• Computer Science
• Quantitative Finance

Take a guided, problem-solving based approach to learning Logic. These compilations provide unique perspectives and applications you won't find anywhere else.

What's inside

• Introduction
• Puzzles and Riddles
• Multi-Level Thinking
• The Rational Detective
• Syllogisms and Sets
• Logic Machines
• Arithmetic With Logic Gates
• Propositional Logic
• First-Order Logic

Joy of Problem Solving

• Intro to Problem Solving
• Coin Rearrangements
• Truth Tellers and Liars
• Operator Searches
• Matchstick Puzzles

Community Wiki

Browse through thousands of Logic wikis written by our community of experts.

• Truth-Tellers and Liars
• Cryptogram - Problem Solving
• Solving Propositional Logic Word Problem
• Mind Reading with Math
• Information Compression
• K-level thinking
• Chess Puzzles
• Arithmetic Puzzles - Operator Search
• Arithmetic Puzzles - Fill in the Blanks
• Elimination Grids
• Grid Puzzles
• Combinatorial Games - Definition
• Combinatorial Games - Winning Positions
• Tic Tac Toe
• Sprague Grundy Theorem
• Chess Puzzles - Reduced Games
• Chess Puzzles - Opening Strategies
• Chess Puzzles - Rook Strategies
• Rook Polynomial
• Game Theory
• Nash Equilibrium
• Zero-Sum Games
• Prisoner's Dilemma
• Braess' Paradox
• Utility Functions
• Cognitive Bias
• Monty Hall Problem
• Birthday Problem
• Two-Envelope Paradox
• Simpson's Paradox
• Berkson's Paradox
• Newcomb's Paradox
• Benford's Law
• Mathematics of Voting
• Survivorship Bias
• Russell's Paradox
• Zeno's Paradox
• Gabriel's Horn
• Truth Tables
• Proof by Contradiction
• Mathematical Logic and Computability
• Mathematical Logic and Computability II (continuation)
• Propositional Logic Using Algebra
• Venn Diagram
• Predicate Logic

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Calcworkshop

A Comprehensive Guide to Logic Master the Basics

Gain a strong foundation in Logic—Improve your analytical skills—Solve complex logical problems

Propositional Logic

1 hr 33 min 25 Examples

• What is a proposition? paradox? open sentence? with Examples #1-9
• What is Symbolic Logic? What are common connectives?
• Negate each statement (Examples #10-13)
• Determine if “inclusive or” or “exclusive or” is intended (Example #14)
• Translate the symbolic logic into English (Example #15)
• Convert the English sentence into symbolic logic (Example #16)
• Determine the truth value of each proposition (Example #17)
• How do we create a truth table? (Example #18)
• Construct a truth table for each statement (Examples #19-20)
• Create a truth table for each proposition (Examples #21-24)
• Form a truth table for the following statement (Example #25)

Logical Implication

1 hr 16 min 15 Examples

• What are conditional statements? Properties? and How do we write them? (Examples #1-2)
• Express each statement using logical connectives and determine the truth of each implication (Examples #3-4)
• Finding the converse, inverse, and contrapositive (Example #5)
• Write the implication, converse, inverse and contrapositive (Example #6)
• What are the properties of biconditional statements and the six propositional logic sentences?
• Write a biconditional statement and determine the truth value (Example #7-8)
• Construct a truth table for each compound, conditional statement (Examples #9-12)
• Create a truth table for each (Examples #13-15)

Logical Equivalence

1 hr 4 min 14 Examples

• What is a Tautology? Contradiction? Contingency?
• How do we show propositional Equivalence? (Examples #1-3)
• Equivalence Laws
• Equivalence Laws for Conditional and Biconditional Statements
• Use De Morgan’s Laws to find the negation (Example #4)
• Provide the logical equivalence for the statement (Examples #5-8)
• Show that each conditional statement is a tautology (Examples #9-11)
• Use a truth table to show logical equivalence (Examples #12-14)

Predicate Logic

1 hr 20 min 23 Examples

• What is predicate logic? What is Quantification? (Examples #1-2)
• Understanding Universal and Existential Quantifiers
• Transform each sentence using predicates, quantifiers and symbolic logic (Example #3)
• Determine the truth value for each quantified statement (Examples #4-12)
• How to Negate Quantified Statements? (Examples #13-14)
• Find the negation of each quantified statement (Examples #15-18)
• Translate from predicates and quantifiers into English (#19-20)
• Convert predicates, quantifiers and negations into symbols (Example #21)
• Determine the truth value for the quantified statement (Example #22)
• Express into words and determine the truth value (Example #23)

Rules of Inference

1 hr 33 min 7 Examples

• Understanding logical arguments
• Inference Rules with tautologies and examples
• What rule of inference is used in each argument? (Example #1a-e)
• Determine the logical conclusion to make the argument valid (Example #2a-e)
• Write the argument form and determine its validity (Example #3a-f)
• Rules of Inference for Quantified Statement
• Determine if the quantified argument is valid (Example #4a-d)
• Given the predicates and domain, choose all valid arguments (Examples #5-6)
• Construct a valid argument using the inference rules (Example #7)

Categorical Syllogism

58 min 12 Examples

• What are the types of propositions, mood, and steps for diagraming categorical syllogism?
• Use Venn diagrams to determine if the categorical syllogism is valid or invalid (Examples #1-4)
• Determine if the categorical syllogism is valid or invalid and diagram the argument (Examples #5-8)
• Identify if the proposition is valid (Examples #9-12)

Chapter Test

1 hr 8 min 9 Practice Problems

• Which of the following is a proposition? (Problem #1)
• Determine the truth value of the given statements (Problem #2)
• Convert each statement into symbols (Problem #3)
• Express the following in words (Problem #4)
• Write the converse and contrapositive of each of the following (Problem #5)
• Decide whether each of following arguments are valid (Problem #6
• Negate the following statements (Problem #7)
• Create a truth table for each (Problem #8)
• Use a truth table to show equivalence (Problem #9)

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Logic Homework Help | Professional Advice and Assistance

You might need logic homework help for varied reasons. But, the major reason why many learners need help with logic homework is the lack of adequate time to complete the assignment. In most cases, this assignment takes a lot of time. And most learners need time to study for exams.

Logic is the study of informal and formal reasoning. Initially, logic was a part of philosophy. However, logic is now a mathematical discipline. It’s a core aspect of computer science and also a linguistic tool. Those studying logic at universities and colleges know what logic in computer science and other disciplines is all about.

Major Reasons to Seek Logic Homework Help

Logic exercises and assignments revolve around argumentative and critical thinking. As a branch in philosophy, logic is a formal study of arguments. Completing assignments in this discipline, therefore, involves defending ideas through logic thinking. You must be smart in presenting ideas and attacking your opponents.

Philosophers, lawyers, policymakers, writers, and editors are all interested in logic and critical thinking. The first philosopher to tackle logic seriously was Aristotle. He coined the word “syllogism”. This refers to a simple argument that lacks a conclusion and two premises yet it can be evaluated for validity and soundness. Essentially, not every syllogism is valid.

Most logic books and classes teach students to come up with valid arguments. They also teach them to consider logical fallacies or errors in thinking carefully. What’s more, students are exposed to different forms of arguments. Symbolic language is learned in logic classes and the best books on logic teach this as well. For instance, learners are taught about symbolic language. This involves arguments that are created with symbols and letters. They resemble different mathematical formulas. But, symbolic logic exercises are not easy.

Some professors require students to argue against all logic in their assignments. Others may require learners to discuss the science of logic extensively. These are not simple tasks. They require time and skills to research and present arguments and counter arguments properly. And because students have tight schedules and deadlines for multiple assignments, they end up seeking help with logic homework.

Using the Logic Homework 8 Inference Rules

Some students turn to experts for logic help because they don’t know how to use the inference rules of logic. In the science of logic, inference rule or the rule of inference is also called the transformation rule. It can be described as a logical form that comprises a function that takes the premises, analyzes the syntax, and then returns a conclusion.

For instance, the inference rule known as Modus ponens involves two premises with one forming the “If p then q” format while the other comes in the form of “p” and “q” as the conclusion. The validity of the rule depends on classical logic semantics and semantics of other non-classical logic. Essentially, if the premises are considered true based on interpretation, the conclusion is also considered true.

Completing homework assignments that require learners to use the 8 inference rules is not easy. It requires the learners to know how old is logic and what the 8 rules stipulate. Essentially, inference rules are templates that build valid arguments.

Inference rules are considered syntactical transform rules that are used to infer conclusions from the premises when creating arguments. These are the rules that people use to infer valid conclusions. These rules are mostly used in math assignments and visual logic puzzle exercises. They also help in forming good arguments in different disciplines and occasions.

Using Logic to Form Excellent Arguments

Logic largely entails studying arguments. People use logic to analyze arguments or reasoning. It’s through logic that experts determine whether an argument is valid or invalid. A good argument is a valid conclusion supported by premises or premises. And, certain rules should be followed to construct logical arguments to minimize errors.

So, how does logic help to form a good argument? Well, you must be familiar with logic rules to form a good argument. Logic means “reason” or “thought”. Therefore, using logic means reasoning or thinking well.

Therefore, a good argument comprises a logical connection between the presented assumptions and conclusion. Those pursuing geometry studies can compare this to writing geometrical proofs. A classic example is the ancient Greeks’ reasoning based on the logic rules.

It goes like this:

• Socrates is a man
• All men are mortal
• Socrates, therefore, is mortal

This makes sense. But, some statements can appear logical when looked at. However, further examination proves that they don’t make sense.

For instance:

• Aristotle and Socrates are different
• Aristotle is, therefore, different from a man

Such an argument doesn’t make sense. It is a logical fallacy or an argument that concludes without following from the presented premises. A fallacy is also defined as faulty or invalid reasoning. It’s an argument that professes decisiveness of an issue yet it is not.

• Logic proofs help in strengthening an argument. To provide these proofs, you must familiarize yourself with the subject that you want to argue about and stick to it. This will enable you to express your reasons for reaching the conclusions that you make. You also present the points that you wish to make in your argument. To be strong, an argument should have a minimum of three main points.
• Practice making an argument from a different viewpoint when preparing for a debate or an argument. This will enable you to consider the counter-arguments that you’re likely to face. This is what most people term as being the devil’s advocate. It’s the practice that lawyers use to prepare for tough cases.
• An argument that considers only one side of an issue can’t win. To come up with a good argument, you must switch from one side to another with ease. Your opponents should not lead or distract you from the topic.
• Additionally, avoid getting emotional when presenting your argument. Avoiding getting emotional can boost logic in an argument. It enables you to remain calm even when your opponent provokes you. To avoid getting emotional, maintain the normal volume of your voice, avoid insults, and expect opposition. Learn to listen to your opponent without losing temper.

Practice Solving a Logic Puzzle

One of the best ways to enhance logical reasoning and arguing is by practicing. Practice constructing logical arguments or playing logic games. For instance, you can practice by arguing about the logic to never do homework. You can also read logic puzzle books before you start solving puzzles.

If you work on puzzles consistently, brain cells’ connections will be reinforced. New brain cells’ connections will also form. And, this will enhance your short-term memory. Memory is very important when it comes to completing puzzles. It enables a person to remember the sizes, shapes, and pieces. This enables you to visualize where different sizes and shapes of the puzzles fit.

What’s more, playing logic games help with focusing, reaction control, and attention. These are important skills when it comes to arguments. But, some logic games and puzzles are not easy. Nevertheless, they play a crucial role in enhancing the ability to make logical arguments with valid conclusions.

Get Professional Assistance

Completing homework in logic requires a vast knowledge of logic traditions. Mathematical notation, logic programming, and incompleteness theorems can also be involved. Essentially, there is so much that is involved when completing logic assignments.

Students must also ensure that their work is not laced with plagiarized content. They must also meet the submission deadlines set by their educators. These are some of the major challenges that prompt learners to turn to experts that require them to simply say, ‘do my logic homework’.

You should get assistance with your homework if:

• You’re confused by multiple writing assignments in logic subjects
• You don’t have adequate time to acquire knowledge on the subjects separately and complete the assignments
• You have more important things to do instead of spending all your time researching, learning, and writing assignments

You can approach professional homework helpers if faced with these and other problems. Your professor, guardians, or friends might not always be available to help with homework or show you how to solve a logic puzzle. However, online logic homework helpers are available 24/7. Contact them if you need help with any logic task.

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How To Find Solutions For Your Logic Homework Problems

Logic homework is difficult, so it’s not surprising if you struggle with it. You’re not alone, though! Many people find it hard to do. And that’s exactly why we’ve written this handy guide to finding solutions for your logic homework problems with ease.

Use your textbook

Your first port of call when you need assistance should always be your textbook, so try looking for the solutions to your logic homework problems there. Even if you don’t find the exact answers, you should find very similar examples with their corresponding answers. And, you can use those to work out the answers for your assignment questions. If you don’t have a decent textbook, it really is worth getting one, as you can consult it every time you get stuck with the work. In addition, you can use it when you study for tests and exams.

Use a decent study guide

Another excellent place to look for assistance is in a good study guide. Like your textbook, it may have similar examples with their corresponding answers. It may even have the exact questions and answers you’re looking for! You can buy a study guide for yourself in reputable bookshop, or even online. You’ll also find that you use your study guide for more than just assignments. Normally, study guides explain work very well, so you can use it to study the theory, too.

Ask your friends

You can also try asking your friends for solutions to your logic homework, as they may have already done the assignments, or even found the solutions somewhere else. Just remember that your friends may not be willing to let you copy their work if they’ve slaved over it themselves.

Look online

A really great place to look for assignment answers is on the Internet, so try searching there. You can look on homework websites, as they often have answers for assignments. In addition, there are many websites dedicated to the study of logic, so you may find some decent answers on those sites, too. Also, don’t forget to check some of the live help websites, as there are so many great people who are willing to give their time to help students with their schoolwork.

Do the work yourself

Even though there are so many excellent places to get solutions for your logic homework, there’s no substitute for actually doing the work yourself. You’ll never learn to do it if you don’t try, so attempt the questions on your own first. Then you can start looking for the answers to check your work.

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Any logic assignment takes a lot of time. This is particularly true for those who also have other things to do besides the Logic assignment. These tasks involve a lot of critical and argumentative thinking but more importantly - explaining the conclusion in the written form. For math, Logic is a core for making one thinking with the A to Z approach, which is why practicing the Logic assignments is a great exercise. However, if you feel stuck with any Logic assignment, our experts can help you out whenever you need for a reasonable price. 

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Logic is a field of mathematics that has its origins in philosophy. It can be defined as the science of formal principles of reasoning or correct inference. Logic had its birth with the Greek philosopher Aristotle whose system of logic is referred to as Aristotelean logic. His form of logic is based upon a collection of treatises known as the Organon. One treatise in this collection, the Prior Analytics , has the most organized discussion of formal logic.

Aristotelean logic begins with the distinction between subject and predicate which is a grammatical concept as well. A subject is defined as an individual entity or a class of entities. A predicate is a property or characteristic of a mode of existence which a given subject may or may not possess. For example, an individual (the subject) can be skillful or not (predicate) and all men (subject) may or may not be brothers (predicate). The basic principles of predication include identity, non-contradiction, and either/or.

Identity simply means that everything is what it is and acts accordingly to its designation. For example, an acorn will only grow into an oak tree. Non-contradiction refers to an object only being able to be one thing and one existence. A predicate cannot belong and not belong to a subject in a given respect at a given time. For example, an honest man cannot also be a thief. Either/or refers to everything being in existence or not being in existence. It may sound complicated but it means that a predicate either belongs or does not belong to a subject in a given respect at a given time. For example, a society can either have its freedom or not have its freedom.

Aristotle believed that the basic unit of reasoning was a syllogism. In basic terms a syllogism denotes a relationship within a group of variables. For example:

Some A are B

All B are C

Therefore, some A are C

Every syllogism consists of two premises and one conclusion. Each premise and its conclusion can be subcategorized into four types. These four types include universal affirmative, or all members of a group are members of another group; universal negative, or no members of a group are members of another group; particular affirmative, or some members of a group are members of another group; and particular negative, in which some members of a group are not members of another group.

Aristotle may be known as the first to devise the idea of logic but the work of Richard Dedekind and Georg Cantor also contributed to what is known as mathematical logic. These two mathematicians reasoned that there are paradoxes within logic. Paradoxes are statements that can be both true and false. However, logic dictates that this assumption cannot be correct. The work of Dedekind and Cantor led to the profession of mathematical logician.

Logic involves both inductive and deductive reasoning. Inductive reasoning is the process by which a conclusion is derived by making limited observations. Deductive reasoning is the process where definitions and facts are used to come up with a particular conclusion. Arguments within logic can be summarized through truth tables that summarize the possibilities of the statements a person is studying, to determine whether they are true or false. When using a truth table, statements and predictions can be replaced with letters and symbols.

• http://www.personal.psu.edu/t20/papers/philmath/
• http://www.math.wichita.edu/history/topics/logic.html

To fulfill our tutoring mission of online education, our college homework help and online tutoring centers are standing by 24/7, ready to assist college students who need homework help with all aspects of logic. Our mathematics tutors can help with all your projects, large or small, and we challenge you to find better online logic tutoring anywhere.

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10: Problem Solving Logic Packet

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• Page ID 59124

• Julie Harland
• MiraCosta College

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• 10.1: George Polya's Four Step Problem Solving Process
• 10.2: Reasoning and Logic Logic is a tool to solve problems. In mathematical logic, a PROPOSITION (or STATEMENT) is a sentence that is either true or false. It cannot be both. One way to think about it is that in order for it to be true, it must be always be true. There can be no qualifiers.
• 10.3: Basic Arguments- Using Logic
• 10.4: Review Exercises

Logic is the study of formal and informal reasoning. Originally a branch of philosophy, logic has also become a mathematical discipline, the core of computer science and a tool of linguistics. If you study logic at college, then you have already understood that expert help with some assignments is essential.

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Logic is the field that studies the various forms of valid inference. Moreover, logic analyzes the laws of truth in great detail. But you already know this and you probably just need some assistance. Do you need logic homework help? Or maybe you just need some information on how to finish your logic homework faster. We can help you with both of these problems. Frankly, logic homework can be quite difficult to do at times. If you need to write an extensive essay on the advantages and disadvantages of artificial intelligence from a logical standpoint, you probably know what we mean. But did you know that you can save a lot of time and effort just by finding some good logic topics?

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Recently Asked Symbolic Logic Questions

• Q 1 : Class Activity 6/28/23 MTH 231, done in class Wednesday, 6/28/23 1. Let r be the proposition "It is raining," s the proposition "The sun is shining," and w the proposition "It is windy." Write the following propositions using r, s, and w and logical connectives. (a) It is windy, and either the sun is shining or it's raining. (b) If it's not raining, then the sun is shining but it's not windy. (c) If it's raining or windy, then the sun is not shining. See Answer
• Q 2 : 2. Let r be the proposition "It is raining," s the proposition "The sun is shining," and w the proposition "It is windy." Express each of the following compound propositions as an English sentence. (a) w V (r^8) (b) r→ (-8 ^ w) (c)¬8 → (w Vr) See Answer
• Q 3 : + A ALEKS-Ahkia Holloway - HW 3.1 X G Write the statement in symbols. L x s.com/alekscgi/x/Isl.exe/1o_u-IgNslkr7j8P3jH-li0BWOJBInLRZL18Trqeg6PUZ9BEvQEFqlFxsjsXHHKJvMnqEfhfiubz6nu28sVwqAJLE60... Q : ch HW 3.1-3.3 Question 10 of 25 (1 point) | Question Attempt: 3 of Unlimited Check Write the statement in symbols. Let p= "Sara is a political science major" and let q = "Jane is a quantum physics major". Jane is a quantum physics major, or Sara is not a political science major. The statement, in symbols, is written as % 9 15 5 10 f6 i 48 6 & 7 AD OVO 0-0 58 f8 8 $ 0 0 0 fg hp ( 9 ((( f10 16 ▷II Ⓒ2023 McGraw Hill LLC. All Rights Reserved. O E ✓ 18 f11 Save For Later ✓ 19 Terms of Use f12 Ahkia ins Espand 8 prt sc © E₂ Submit Assignment K Privacy Center Accessibility 91°F Windy delete backsp See Answer
• Q 4 : x A ALEKS - Ahkia Holloway - HW 3.1 x Ⓒ Write the statement in symbols. x + aleks.com/alekscgi/x/Isl.exe/1o_u-IgNslkr7j8P3jH-liOBWOJBInLRZL18Trqeg6PUZ9BEVQEFqlFxsjsXHHKJ ||| Question 14 of 25 (1 point) | Question Attempt 4 of Unlimited T Construct a truth table for ~ 9 →p. Use T for true and F for false. P 9 -9--P 0 O B IL @ check 9 T T 10 3 (3 (9 ( -0 0-0 0-0 CAS 40 14 16 16 CANET MEGEN HULIC See Answer
• Q 5 : ALEKS - Ahkia Holloway - HW 3.1 X GWrite the statement in symbols. 1 X + n/alekscgi/x/Isl.exe/1o_u-lgNslkr7j8P3jH-li0BWOJBInLRZL18Trqeg6PUZ9BEvQEFqlFxsjsXHHKJvMr ||| HW 3.1-3.3 Question 15 of 25 (1 point) | Question Attempt: 1 of Unlimited Construct a truth table for (p ✓ q) ^ (g ^ p). Use T for true and F for false. Pq (pvq) ^ (g ^p) L T IL F TI T 9 Check LL D 0 D 21 20 19 -0 0-0 0-0 9 58 O HINT hp 15 © 2023 McGraw Hit LLC. All Rights Res See Answer
• Q 6 : leks.com/alekscgi/x/Isl.exe/1o_u-IgNslkr7j8P3jH-liOBWOJBInLRZL18Trqeg6PUZ9BEVQEFqlFxs search ||| HW 3.1-3.3 Question 16 of 25 (1 point) | Question Attempt: 2 of Unlimited 1 IL • P 9 7 9 → p) ~ p) ~ ~r U F 11 Construct a truth table for (9 → p) ✓ ~ 7. Use T for true and F for false. II IL F Checkk L IL IL T 11 L T UL T 9 F HW 3.1 X GWrite the statement in symbols. L X + F F Af 10 G ☐ 0 [ U 1 - 11 ✓ 12 -0 0-0 0-0 DvC DAD X ✓ 13 58 14 © 2023 McGraw See Answer
• Q 7 : A ALEKS-Ahkia Holloway - HW 3.1 x Ⓒ Write the statement in symbols. L x | + om/alekscgi/x/Isl.exe/1o_u-IgNslkr7j8P3jH-li0BWOJBInLRZL18Trqeg6PUZ9BEVQEFqlFxsjsXHHKJvMnqEfhfiubz III ( Question 9 of 25 (1 point) | Question Attempt: 6 of Unlimited Check 10 ✓11 The statement, in symbols, is written as I ✓12 Write the statement in symbols. Let p= "Sara is a political science major" and let q = "Jane is a quantum physics major". Sara is a political science major, and Jane is a quantum physics major. DAD OVO C-0 -0 X D 6 9 15 0 THE BENE 7 ✓18 2023 McGraw Hu LLC. All Rights Reserved. See Answer
• Q 8 : Exercise 4. In the definition of the nested sequence of A's in the preceding proof, we did not write: Ait1 [A₁U {4₁} A; U{-₁} if A, U {₁} is finitely satisfiable, if A, U{-₁} is finitely satisfiable. Explain why. Hint: Exhibit a set I of wff's and a single wffy such that both IU {p} and TU{-} are satisfiable. See Answer
• Q 9 : Exercise 17 (Cliques in Simple Graphs, III). This continues the examination of the clique problem in Example 15 and Exercise 16. We say that a set A of propositional wff's is satisfied by G iff, for every & A, it is the case that is satisfied by G. The latter notion is defined in Example 15. Let k> 1 be fixed. Show that it is possible to define an infinite set I'(G) of propositional wff's over the set of variables X (as defined in Example 15) such that for every simple graph G, finite or infinite, it is the case that I'(G) is satisfied by G iff G does not contain a k-clique. Thus, the absence of k-cliques in a graph G, finite or infinite, can be expressed by a set I(G) of propositional wff's. Note the contrast with the conclusions in Example 15 and Exercise 16, where it is pointed out that the presence of k-cliques in an infinite graph G cannot be expressed in PL, whether by a single wff or by a set of wff's. Hint: If G does not contain a k-clique, then it does not contain a k'-clique for every k'> k. You need to show that every finite subset of I'(G) can be satisfied, and then invoke Compactness. See Answer
• Q 10 : Exercise 21 (Vertex Coloring in Simple Graphs). All graphs G = (V, E) in this exercise are simple, finite or infinite. Once more, we take the set V of vertices as an initial fragment of the positive integers {1,2,...}, finite or infinite, and its set of edges E CV X V. Such a graph G is said k-colorable if it is possible to assign only one of k colors to every vertex of G such that the two endpoints of every edge are assigned different colors. A famous (and very difficult to prove) result of graph theory is that every finite planar graph is 4-colorable. In this exercise you are asked to show that this result can be extended to infinite planar graphs using Compactness for PL. Let k> 1 be fixed, the number of available colors. For convenience, use two separate sets of propositional variables, Q and C, instead of P: def def {9₁.j|i,j€ {1,2,...}} and C f {ci € {1,2,...} and 1 ≤ j≤ k}. All wff's in this exercise should be in WFFPL (QUC). Use variables in Q to model a given graph G: there is an edge connecting two distinct vertices i and jiff qij is set to truth value true. Use variables in C to model G's coloring: vertex i is assigned color j = {1,...,k} iff is set to truth value true. There are three parts in this exercise, the first two are not limited to planar graphs: 1. Let G = (V, E) be a finite simple graph. Write a wff (G) which is satisfied iff G is k-colorable. Hint: Define (G) in two parts, one part specifies the structure of G (including conditions that there are no self-loops and that G is undirected), and one part specifies that G is k-colorable. You will find it useful to review Example 20. 2. Let Gf (V, E) be an infinite simple graph, with V = {1,2,...}. Show that G is k-colorable iff every finite subgraph of G is k-colorable. Hint: If an infinite G is k-colorable, then so is every finite subgraph of G. This is the easy implication. Compactness for PL should give you the converse, after writing an infinite set Þ(G) of wff's in WFFPL (QUC) expressing the k-colorability of G. 3. Let G = (V, E) be an infinite planar graph, with V = {1,2,...}. Invoke the preceding part to conclude that G is 4-colorable. See Answer
• Q 11 : Exercises 1.5 1. Show that a formula is valid iff T = 0, where T is an abbreviation for an instance p V -p of LEM. 2. Which of these formulas are semantically equivalent to p → (q V r)? (a) qv (-p Vr) (b) q^-r-p (c) p^rq * (d)¬q^r-p. 3. An adequate set of connectives for propositional logic is a set such that for every formula of propositional logic there is an equivalent formula with only connectives from that set. For example, the set {-, V} is adequate for propositional logic, because any occurrence of A and → can be removed by using the equivalences → ¬V and o^= -(-V¬). (a) Show that {¬, ^}, {¬,→} and {→,1} are adequate sets of connectives for propositional logic. (In the latter case, we are treating as a nullary con- nective.) (b) Show that, if C C {¬, ^, V, →, 1} is adequate for propositional logic, then ¬EC or LEC. (Hint: suppose C contains neither nor and consider the truth value of a formula o, formed by using only the connectives in C, for a valuation in which every atom is assigned T.) (c) Is {,} adequate? Prove your answer. See Answer
• Q 12 : Exercise 8. We can restrict the logical connectives to {, V, A}. The set of propositional vari- ables is again P = {po,P1, P2,...}, which is countably infinite. Suppose we extend this syntax with two new connectives, denoted W and M, each taking as a single argument a countably infinite set of previously defined wff's. The resulting syntax is one version of Infinitary PL. If I is the countably infinite set {91, 92, 93,...), then WI can be informally understood as: Wr = 41 V 4₂ V 43 V..., and similarly for Mr. Keep in mind that "41 V 42 V 43 V..." is not a legal formal expression; we use Was a unary connective, applied to a single argument which must be a set, and similarly for . There are three parts in this exercise: 1. Define the syntax of Infinitary PL, preferably in an extended BNF (Backus-Naur Form). Try to be as precise as you can, paying special attention to the presence of ellipses "..." in the definition - or can you think of a formulation that avoids any mention of ellipses? 2. Define the semantics of Infinitary PL, by structural induction on the syntax in Part 1, starting from an assignment of truth values to every member of P (for the base case of the induction). 3. Show that Theorem 2 does not hold, and therefore nor does Corollary 7, for Infinitary PL. Hint: Define a countably infinite set I of wff's such that every finite To CI is satisfiable, but I is not. Further Hint: Include wff = W{-Po: P₁, P2,...} in your proposed r. Remark 9. The infinitary propositional logic (Infinitary PL) extends finitary propositional logic, which is just what is commonly called propositional logic (our PL here). The distinction between infinitary and finitary extends to other formal logics and their proof systems besides PL. You can take the phrase "finitary proof system" to qualify a system that generates new finite expressions (e.g., the sequents of PL in natural-deduction style or the wff's of propositional logic in Hilbert- or Frege-style) from previously generated ones by means of finitely many rules that require each finitely many premises or antecedents - without using any notion of infinite sequence or any notion of infinite set.9 See Answer
• Q 13 : 16 Exercise 27 (Queens Problem). The n-Queens Problem is the problem of placing n queens on an nxn chessboard so that no two queens can attack each other. A solution of the problem when n-6 is shown on the left of Figure 1.2. In this exercise we specify the requirements of a solution for the n-Queens Problem as a propositional wif , with one such wff for every n 4. (There are no solutions for n-2 and 3.) For convenience, we use a set of doubly-indexed propositional variables, instead of P, where the indices range over the positive integers: Q={LJE(L2}}- The desired wif, in this exercise is in WFF(Q). We set the variable to truth value trae (resp. false) if there is (resp. there is not) a queen placed in position (i, j) of the board, where we take the first index i (resp. the second index j) to range over the vertical axis downward (resp. CHAPTER 1. PROPOSITIONAL LOGIC the horizontal axis rightward); that is, i is a row number and j is a column mmber. There are four parts in this exercise: 1. Write the wife and justify how it accomplishes its task. Hint: Write as a conjunction (a) (b) (e) (d) Aqide Age, where is satisfied if there is exactly one queen in each row, is satisfied if there is exactly one queen in each column, is satisfied if there is at most one queen in each diagonal, is satisfied if there is at most one queen in each antidiagonal. Further Hist: Given any two distinct positions (is, ji) and (ia, ja) along a diagonal, it is always the case that is −j 12-ja. And if the two positions are along an antidiagonal, then it is always the case that i, +₁=₂+/ 2. Imagine now an infinite chessboard, which occupies the entire south-east quadrant of the Cartesian plane. The coordinates along the vertical and horizontal axes are, respectively, i (increasing downward) and j (increasing rightward), both ranging over the positive integers (1,2,...). In an attempt to repeat the argument in Example 20 and Exercise 21, someone once defined the set of wis {n>4), and wrote the following (in outline here): The set I is finitely satisfiable and, therefore, satisfiable by Compactness. Hence, there exists a solution of the Infinite Queens Problem, which satisfies conditions {(a), (b), (c), (d)) for all 4. 3. Your task is to define an infinite set that: What is wrong with the preceding argument? The answer is subtle and you need to be careful. (₁|k> 1} of distinct propositional weff's such (a) For every > 1 there is n1 such that satisfaction of wff 8, implies satisfaction of wif, defined in part 1 of this exercise, ie, satisfaction of 6, defines a solution of the x-Queens Problem. (b) For all >k> 1, if satisfaction of welf's By and define solutions of the n'-Queens Problem and Queens Problem, respectively, then n²>n. (e) Every finite subset ofis satisfiable. Hint: For part (a), make 8 define a particular n-Queens Problem, ie, is satisfied by exactly one truth assigment of the variables occurring in 6. For (b) and (c), read and understand the subsection entitled "A second solution of the infinite Queens Problem" in Appendix G. 4. Let be the infinite set of weff's defined in the preceding part. Use Compactness for PL to give a rigorous argument that the Infinite Queens Problem has indeed a solution. 0 See Answer
• Q 14 : Exercise 1. Write a natural-deduction ₁ (p^q^r) → (PV¬qV¬r) This is a more general version of de Morgan's law (4). 2. Write a natural-deduction proof of the most general de Morgan's law (4): 42 = (P₁ ^^ Pn) → (P₁ VV-pn) where n > 2. proof of the following WFF: See Answer
• Q 15 : Question: The last question I ask in your notes is as follows: The big question: What's the main message or idea you picked up from the story? Again, this is called the central idea that you determine. Think of the title, plot, characters, literary devices, and other ideas we discussed. I expect a well-developed paragraph that discusses what you feel is the main idea AND how the story supports your interpretation. Story: https://www.commonlit.org/en/texts/home-1 Just answer in 150 words See Answer
• Q 16 : Problem 1 There are two parts: [Lecture Slides 10, page 18]: (a) Prove one side of the equivalence in the exercise in [Lecture Slides 13, page 32], specifically Þ→ V (not V Þ), after replacing and ; by propositional variables p and q₁, for i = 1, 2, 3. (b) Prove one side of the equivalence in the exercise in [Lecture Slides 13, page 33], specifically Þ→ V (not $), after replacing , and ; by propositional variables p; and qi, for i = 1, 2, 3, but leave as a generic (i.e., unknown) wff with two free variables. In both parts, we ask you to choose a proof-theoretic, not semantic, approach. Proof-theoretically, you can choose natural deduction or also tableaux, even though in the case of tableaux we have not yet mentioned expansion rules for quantifiers in lecture (but these are easy to formulate - left to you!). O See Answer
• Q 17 : Exercise 126 (Hilbert-styles vs. Natural Deduction). Read Exercise 125, without necessarily solving it, before you attempt this one. The preceding exercise proposes a strictly proof-theoretic approach to showing that a Hilbert-style proof system and a natural-deduction proof system have equal deductive power. In this exercise we consider an alternative semantic approach, which invokes Soundness and Completeness for both proof systems. Specifically, each of the two sys- tems as here presented is sound and complete relative to the standard (classical) semantics of propositional logic based on Boolean algebras. There are three parts in this exercise, the first two of which are just plans in outline to prove the equivalence of the two systems: 1. If I, then I by Soundness of the Hilbert system. By Completeness of the natural deduction system, it follows that I END 4. 2. If I END 4, then I by Soundness of the natural deduction system. By Completeness of the Hilbert system, it follows that I ₁9. Provide the details of the two preceding parts, given only in outline here, pointing out missing prerequisites (e.g., we do not prove Soundness and Completeness for the Hilbert system in these notes) and propose ways of filling the gaps and how to prove them. (We do not add subscripts "H" and "ND" to "", because the two systems are sound and complete relative to the same semantics.) 3. Compare and discuss the pros and the cons of the proof-theoretic approach in Exercise 125 and the approach in this Exercise 126 which makes a detour through semantics. 0 See Answer
• Q 18 : Exercise 144. Let R be a binary relation symbol and f a unary function symbol. def 1. Show that the sentence of Vr R(x, f(x)) → Vry R(x, y) is valid. Do it in two different ways: (a) proof-theoretically, p, using natural deduction, and (b) semantically, = 4. def 2. Show that the sentence Valy R(x,y) → Vr R(x, f(x)) is not valid. Note that is just the converse implication of . Hint: Try a semantic approach, i.e., show. You need to define a structure A so that the left-hand side of "" in is true in A but the right-hand side of "" is false in A. 3. Conclude that Vrly R(x, y) and Vr R(x, f(x)) are not equivalent first-order wff's. Remark: Despite the conclusion in part 3, Proposition 142 asserts Vray R(x, y) and Vr R(x, f(x)) are equisatisfiable, i.e., if there is a model for one, then there is a model for the other, and vice- versa. 42 Review the definition of o[a] in Section B.3. See Answer
• Q 19 : 36 The next proof makes explicit reference to notions in topology. As indicated in the preceding alternative proof, a truth assignment can be denoted by a path in the full binary tree Tall, now viewed as an w-sequence in the product space (T,F). (We write for the first infinite ordinal, which is the set of natural numbers listed in their standard order.) We view {T,F) as the underlying space of a product topology ({T,F)", O), thus making every truth assignment a "point" in that topology. O is a family of open sets that define the topology, which are in this case subsets of points in {T, F)~ and satisfy the usual requirements of a topology: • The empty set and the full space {T,F) are in O. • O is closed under arbitrary unions, • O is closed under finite intersections. We can define a subset UC {T,F}" to be open iff there is a finite set of indices IC such that: U = II { Ai | i €w and A; C {T,F}} where A. = {T,F) for every i Ew-I. In words, in the infinite product U = Ao × A₁ × --- × A; x--, for all but finitely many indices i it is the case that A; = {T,F). A set U C {T,F)" is closed iff it is the complement of an open APPENDIX F. ALTERNATIVE COMPACTNESS PROOFS set. In the case of the product topology, every open subset UC (T,F) is also closed, and thus called clopen. Let A be a subset of (T,F). An open covering of A is a family of open sets {U; | i I} CO such that A CU{U; i 1}. And A is said compact if every open covering of A has a finite subcovering; i.e., there exists a finite subfamily U₁₁, UU₁ of (U; | i I} such that A (U₁, UU, U...UU.). By Tychonoff's Theorem in topology, the product topology ({T,F), O) is compact, which means that every open covering of a subset of points AC {T,F) has a finite subcovering. Alternative Proof II of Theorem 2 (Compactness for Propositional Logic). Again here, we only need to consider the non-trivial implication "+": If I is finitely satisfiable, then I is satisfiable. For every propositional wffy, let A, C {T,F}" be the collection of all points/truth assignments that satisfy p. The set A, is a closed (and open) subset of {T,F}" in the topology ({T,F)",0), which follows from the fact that only mentions finitely many propositional variables. It is easy to check that, for every finite subset A of I, if A is satisfiable, then {A | A} is not empty. Hence, the family of closed sets {Apyr} satisfies the finite intersection property. Moreover, the product topology ({T.F),O) is compact, as noted above. Hence, {A, ET) is not empty, which is the desired conclusion. 0/nExercise 147. This exercise is couched in a language which is a little more familiar to computer scientists. Given a set IWFF₁(P), the binary tree T(I) induced by I' is defined in the 35 proof above. In T(I), every finite path is a finite sequence, and every infinite path is an infinite sequence, where all the entries are in {T,F). The set of all such finite sequences is denoted {T,F)", and the set of all such infinite sequences is denoted {T,F). The root node of T(I) is represented by the empty sequence e, every leaf node is connected to the root node by a finite path, and every infinite path is one that can be traversed without ever reaching a leaf node. An arbitrary binary tree can therefore be represented by a subset of {T, F}*U{T,F}", satisfying two conditions: • U is prefix-closed, i.e., for every (possibly infinite) path ₁ € {T,F)* U{T,F) and every finite path #₂ € {T,F)", if ₁ EU and ₂ is a prefix of ₁, then #₂ EU. • For every finite path = {T,F)", it holds that T U iff F EU, i.e., every non-leaf node has two immediate successors. Given an arbitrary IWFF (P), let T(T) be the subset of infinite paths in T(I): T(T) = T(r)n(T.F)". By the preceding proof, T. (T) ‡ Ø iff the set I is satisfiable. Let To, F₁, and I2, be defined as follows: To = {-P₁ ^P₂}, T₁ = {P₁ → (P₂A---A-PE) | A>2}, del 1₂ = {~-P₁ → (P²2 A---A-¬-Pk) |>2}. There are two parts in this exercise: 1. Define the sets of infinite paths T. (To), T.(₁UF₂), and T(Tour₁ UF₂) as subsets of {T,F). In your answers, use the notational conventions of regular languages and regular w-languages that we have used earlier in the presentation of this exercise. 2. For each of the three sets defined in part 1, explain how they indicate whether the corre- sponding set of wff's is satisfiable or not. You will find it useful to consult Figure F.1. 0 See Answer
• Q 20 : In this assignment, you will use what you learn in Logic module to: Create a compound statement that contains at least 2 connectives (negation, conjunction, disjunction, conditional, biconditional). Express the compound statement in the symbolic form. Construct a truth table for the compound statement that you created. See Answer

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