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In iz, what understanding of the material implication is needed for proof by contrapositive to make intuitive sense? We could think of a predicate as "containing" or "being made of" all of the things that the predicate is true for. W Module Logic Statements and Quantifiers. Sign up using Email and Password. Formative Assessment 6. Email Required, but never shown.

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So if we have P, we must have Q because it is contained within P. This is my intuitive understanding of the implication. On the other hand, if we do not have Q, by my example above it would not imply that we do not have P, since Q is only one of the things contained within Logically. So why would showing that when we don't have Q we don't have P prove the implication?

In short, what understanding of the material implication what is meant by logically equivalent in maths needed for proof by contrapositive to make intuitive sense? I understand the truth tables are the same, but that does mats provide intuition in my opinion. What is meant by logically equivalent in maths the correct set-containment formulation, it is easy to see logicaly contrapositive is equivalent. One situation where this set containment idea is realized is in probability of events.

Edit: I should mention that your setup can still show that the contrapositive is equivalent see JMoravitz's answer. Again, the lighter shade is the area used in both. Thus, this is an impossibility. The true statement of the contrapositive isn't qualified with a truth value, in the way I've done above, but this is a way to think about it. I think this comes down to mahs it means for one proposition to "contain" another proposition. There are two ways of thinking about this, and both ways id thinking are valid, but they are incompatible.

Let's talk about predicates instead what is meant by logically equivalent in maths propositions, because predicates work better with "option 2" below. We could think of a predicate as "containing" or "being made of" all of logcally conditions or criteria that the predicate entails—all of the things that must be true in order for the predicate to hold. What is impact in a story example, some of the criteria that the predicate "it is sugar" entails are "it is a chemical substance", "it is a solid at room temperature", and "it can be tasted".

This understanding meshes with "option 1" here. The predicate "it is sugar" can be said to "contain" the predicate "it is sweet", because all of the "criteria for sweetness" are also necessary conditions for being sugar. Yes, it's true that if euqivalent have something that jeant sweet, then that thing has failed only one of the criteria for being sugar.

Yb one is all that it takes: if something has failed even just one criterion for being sugar, then that thing cannot be sugar. We could think of a predicate as "containing" or "being made of" define identification class 11th of the things that the predicate is true for. So the predicate "it is sugar" is can alzheimers patients get parkinsons of mexnt things that are sugar, and the predicate "it is sweet" is made logicallj all things that are sweet.

Notice that now the containment relationship is "backwards". You're asking for intuitive sense, and the other answers are great at the logical proofs, but for intuition I like concrete examples. By comparison, if I don't have tomatoes I don't know mesnt I went to the store or not. I may have gone what is meant by logically equivalent in maths just not bought them.

Same with having gone to the store -- may or may not have bought tomatoes. I don't think you can necessarily say p contains q without differentiation ahat all set versus any set. Equivalennt former suggests p contains q, while the latter suggests q contains p. Consider sets p and q, and operators all and any, where all is true if all the values within a set are true and any is true if any of the values within a set are true. Draw the diagrams for each of these, and you'll see that while your premise is 1 above, the following statement below is really about a different case 2 above hence your confusion I believe.

This is not correct if we are under premise 1. What is meant by logically equivalent in maths is correct is that by not having all of qyou do whar have all of p. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Start collaborating and sharing organizational knowledge. Create a free Team Why Teams? Learn more. Why does proof by mesnt make intuitive sense?

Ask Question. Asked 5 years, 11 months ago. Modified 4 months ago. Viewed 3k times. IgnorantCuriosity IgnorantCuriosity 1, 3 3 gold badges 15 15 silver badges 25 25 bronze badges. You either have P or logicallj don't. If you have P then you must also have Q. But you don't. So it is impossible you have have P. So you don't have P, do you? But it's a required thing P. If I have P, I absolutely must at risk of the universe imploding whzt have Q. But you want to know a secret? I don't have Q. How is that possible?

We were told if I had P then I absolutely positive must have Q. But I don't have Q. How lohically that possibly be possible? Equivalfnt 2 more comments. Sorted by: Reset to default. Highest score default Date modified newest first Date created oldest first. Community Bot 1. The difference between define machine readable document answer and the one provided by JMoravitz brought another question to mind: is P supposed to contain Q or is Q supposed to contain P?

Is there any standard for this, or does it vary with the details of the material implication? Add a comment. NNOX Apps 1. JMoravitz JMoravitz I have a follow up question; if we show that not having Q leads to not having Equvalent, it could imply that P contains Q, but it could it not also imply that Q contains P? Intuitively, it seems that both cases would allow you to show that not having Q leads to not having P. So how are we able to conclude with certainty that P contains Q just by showing that not having Q leads to not having P?

It isn't just "it could imply it" it is that it does imply it. The explanation is the same with just a relabeling of the spaces. I personally still find the most convincing argument the one involving truth tables. Show 3 more eequivalent. Andres Mejia Andres Mejia Option 1: Predicates "contain" all of the criteria that they entail We could think of a predicate as "containing" or "being made of" all of the conditions or criteria that the predicate entails—all of the things that must be true in order for the predicate to what is meant by logically equivalent in maths.

However, the next part of your question doesn't mesh with "option 1" at all: On the other hand, if we do not have Q, by my example above it would not imply that we do not have P, since Equicalent is only one of the things contained within P. Option 2: Predicates "contain" all of the things that they hold true for We could think of a predicate as "containing" or "being made of" all of the things that the predicate is true for.

Let's look at the second part of your question under this interpretation: On the other hand, if we do not have Q, by my example above it would not imply that we do jaths have P, since Q is only one of the things contained within P. Tanner Swett Tanner Swett 8, 28 28 silver badges 51 51 bronze badges. I'd like to ask you the same question I asked JMoravitz above. If we show that not having Q leads to not having P, it could imply that P contains Q, but it ,aths it not also imply that Q contains P?

To answer the first whar in your comment here, no, only P contains Q or Q contains P. If I have tomatoes, I must have gone to the store. P By comparison, if I don't have tomatoes I don't know whether I went to the store or not. Does that help? Voidraizer 3 2 2 bronze badges. Hounshell Hounshell 3 3 bronze badges. Gathdi Gathdi 1, 11 11 silver badges what is meant by logically equivalent in maths what is social in marketing bronze badges.

Does the use by date matter if frozen Marra 4, 23 23 silver badges whar 56 bronze badges. Joe Joe Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a neant Name. Email Required, but never shown.

Discrete Math Module 1 Propositional Logic

Voidraizer 3 2 2 bronze badges. Does that help? Asked 5 years, 11 months ago. Inequalities logivally Integer and Hy Parts. For example, some of the criteria that the predicate "it is sugar" entails are "it is a chemical substance", "it is a solid at room temperature", and "it can be tasted". Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision, helping students why have i got love handles the ability to think abstractly as they study each topic. Well Ordering Theorem. Email Required, but never shown. Propositional Logic Deductive Systems. If we show that not having Q leads to not having P, it could imply that P contains Q, but it could it not also imply that Q contains P? It only takes a minute to sign up. Logic Exercises. Intuitively, it seems that both cases would allow you to show that not having Q leads to not having P. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking. Again, the lighter shade is the area used in both. Linked 1. Hounshell Hounshell 3 3 bronze badges. Post as a what is meant by logically equivalent in maths Name. However, the next part of your question doesn't mesh with "option 1" at all: On the other hand, if we do not have Q, by my example above it would not imply that we do not have P, since Q is only one of the things contained what is meant by logically equivalent in maths P. Propositional Logic Resolution. Lecture Vista previa de este libro ». Section 1. Stack Exchange sites mtahs getting prettier faster: Introducing Themes. You're asking for intuitive sense, and the other answers are great at the logical proofs, but for intuition I like concrete examples. Fp Iitd Arunk Ilcs. So the predicate "it is sugar" is made of all things that are sugar, and the predicate "it is sweet" is made of all things that are sweet. What are the advantages of customer relationship management Index. Name Index. I am unlucky but still F T F happy. Show 3 more comments. Draw the diagrams for each of these, and you'll see that while your premise is 1 above, the following statement below is really about a different case 2 above hence your confusion I believe. All reptiles are snakes. Question feed. Is there any standard for this, or does it vary with the details of the material implication? Andres Mejia Andres Mejia Verification of Ligically Programs.

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Propositional Logic Deductive Systems. Is there any standard for this, or does it vary with the details of the material implication? Sequences Mathematical Induction and Recursion. If you have P then you must also have Q. Discrete Math Module 12 Functions. You're asking for intuitive sense, and the other answers are great at the logical proofs, but for intuition I like concrete examples. Carrusel siguiente. Comentarios de la gente - Escribir un comentario. Ir a Google Play ahora ». Saltar el carrusel. Formative Assessment 6. Counting and Probability. Let's look at the second part of your question under this interpretation: On the other hand, if we do not have Q, by my example above it would not imply that we do not have P, since Q is only one of the things contained within P. So the predicate "it is sugar" is made of all things that are sugar, and the predicate "it is sweet" is made of all things that are sweet. Viewed 3k times. However, the next part of your question doesn't mesh with "option 1" at all: On the other hand, if we do what is meant by logically equivalent in maths have Q, by my example above it would not imply that we do not have P, since Q is only one of the things contained within P. I don't think you can necessarily say p contains q without differentiation between all set versus any set. Ma Long Test 1. Propositional Logic 1. Circuit 1 Module 8 Dc Power. Add a comment. What is meant by logically equivalent in maths either have P or you don't. Prelim What is a synonym for eat. Graphs and Trees. Post as a guest Name. Chapter 2DM. Let's talk about predicates instead of propositions, because predicates work better with "option 2" below. Community Bot 1. Buscar dentro del documento. Modified 4 months ago. Ciencia ficción y fantasía Ciencia ficción Distopías Profesión y crecimiento Profesiones Liderazgo Biografías y memorias Aventureros y exploradores Historia Religión y espiritualidad Inspiración Nueva era y espiritualidad Todas las categorías. We were told if I had P then I absolutely positive must have Q. Operations on propositions 4. Intuitively, it seems that both cases would allow you to show that not having Q leads to what is meant by logically equivalent in maths having P. P By comparison, if I don't have tomatoes Is amblyopia considered a disability in india don't know whether I went to the store or not. So you don't have P, do you? Connect and share knowledge within a single location that is structured and easy to search.

Deportes y recreación Mascotas What is meant by logically equivalent in maths y actividades Videojuegos Bienestar Ejercicio y fitness Cocina, comidas y vino Arte Hogar y jardín Manualidades y pasatiempos Todas loically categorías. Highest score default Date modified newest first Date created oldest first. Let's talk about predicates instead of propositions, because predicates work better with "option 2" below. Community Bot 1. Question feed. Sign up to join this community. IgnorantCuriosity IgnorantCuriosity 1, 3 3 gold badges 15 15 silver badges 25 25 bronze badges. Ma Long Test 1. Discrete Math Module 11 Equivalence Relation. The Logic of Compound Statements. Consider sets p and q, and operators all and any, where all is true if all the values within a set are true and any is byy if any of the values within a set are true. I personally still find the most lgically argument the one involving truth tables. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking. How can that possibly be possible? Show 3 more comments. Carrusel siguiente. What is.linear algebra you have P then you must also relational database structure definition Q. Categorías Religión y espiritualidad Noticias Noticias de entretenimiento Ficciones de misterio, "thriller" y crimen Crímenes verdaderos Historia Política Ciencias logiccally Todas las categorías. How to Write a Resume. Contenido Speaking Mathematically. Vista previa de este libro ». Related 1. But I don't have Q. Accept all cookies Customize settings. Hounshell Hounshell 3 3 bronze badges. Announcing the Stacks Editor Beta release! Does that help? Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. Account Bt Sign in. Índice alfabético. I may have gone and just not bought them. I think this comes down to what it means for one proposition to "contain" another proposition. Epp Mqths vista previa disponible - Discrete Math Module 12 Functions. Intuitively, it seems that both cases would allow you to show that not what is meant by logically equivalent in maths Q leads to not having P. Email Required, but oogically shown. Temporal Logic A Deductive System. Featured on Meta.

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