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Converse, Inverse, and Contrapositive Examples (Video) The contrapositive is logically equivalent to the original statement. }\) The contrapositive of this new conditional is \(\neg \neg q \rightarrow \neg \neg p\text{,}\) which is equivalent to \(q \rightarrow p\) by double negation. Mathwords: Contrapositive Contrapositive Switching the hypothesis and conclusion of a conditional statement and negating both. The G The positions of p and q of the original statement are switched, and then the opposite of each is considered: q p (if not q, then not p ). Converse statement is "If you get a prize then you wonthe race." If a quadrilateral does not have two pairs of parallel sides, then it is not a rectangle. 5.9 cummins head gasket replacement cost A plus math coach answers Aleks math placement exam practice Apgfcu auto loan calculator Apr calculator for factor receivables Easy online calculus course . A statement which is of the form of "if p then q" is a conditional statement, where 'p' is called hypothesis and 'q' is called the conclusion. The conditional statement is logically equivalent to its contrapositive. Contrapositive Proof Even and Odd Integers. (P1 and not P2) or (not P3 and not P4) or (P5 and P6). This is the beauty of the proof of contradiction. If it rains, then they cancel school Suppose if p, then q is the given conditional statement if q, then p is its converse statement. The contrapositive version of this theorem is "If x and y are two integers with opposite parity, then their sum must be odd." So we assume x and y have opposite parity. Related to the conditional \(p \rightarrow q\) are three important variations. In addition, the statement If p, then q is commonly written as the statement p implies q which is expressed symbolically as {\color{blue}p} \to {\color{red}q}. E A \rightarrow B. is logically equivalent to. What Are the Converse, Contrapositive, and Inverse? Select/Type your answer and click the "Check Answer" button to see the result. If \(f\) is not differentiable, then it is not continuous. open sentence? Retrieved from https://www.thoughtco.com/converse-contrapositive-and-inverse-3126458. To create the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion. In Preview Activity 2.2.1, we introduced the concept of logically equivalent expressions and the notation X Y to indicate that statements X and Y are logically equivalent. There is an easy explanation for this. Step 2: Identify whether the question is asking for the converse ("if q, then p"), inverse ("if not p, then not q"), or contrapositive ("if not q, then not p"), and create this statement. What is Quantification? - Converse of Conditional statement. If n > 2, then n 2 > 4. When you visit the site, Dotdash Meredith and its partners may store or retrieve information on your browser, mostly in the form of cookies. Now you can easily find the converse, inverse, and contrapositive of any conditional statement you are given! The original statement is the one you want to prove. "If we have to to travel for a long distance, then we have to take a taxi" is a conditional statement. Let us understand the terms "hypothesis" and "conclusion.". Whats the difference between a direct proof and an indirect proof? Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. FlexBooks 2.0 CK-12 Basic Geometry Concepts Converse, Inverse, and Contrapositive. In other words, the negation of p leads to a contradiction because if the negation of p is false, then it must true. If \(f\) is continuous, then it is differentiable. It turns out that even though the converse and inverse are not logically equivalent to the original conditional statement, they are logically equivalent to one another. Contrapositive definition, of or relating to contraposition. The statement The right triangle is equilateral has negation The right triangle is not equilateral. The negation of 10 is an even number is the statement 10 is not an even number. Of course, for this last example, we could use the definition of an odd number and instead say that 10 is an odd number. We note that the truth of a statement is the opposite of that of the negation. You don't know anything if I . ", Conditional statment is "If there is accomodation in the hotel, then we will go on a vacation." Warning \(\PageIndex{1}\): Common Mistakes, Example \(\PageIndex{1}\): Related Conditionals are not All Equivalent, Suppose \(m\) is a fixed but unspecified whole number that is greater than \(2\text{.}\). Tautology check The addition of the word not is done so that it changes the truth status of the statement. 2023 Calcworkshop LLC / Privacy Policy / Terms of Service, What is a proposition? Thus. What Are the Converse, Contrapositive, and Inverse? Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation. Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic. Let x and y be real numbers such that x 0. Suppose that the original statement If it rained last night, then the sidewalk is wet is true. Here 'p' is the hypothesis and 'q' is the conclusion. Learn from the best math teachers and top your exams, Live one on one classroom and doubt clearing, Practice worksheets in and after class for conceptual clarity, Personalized curriculum to keep up with school, The converse of the conditional statement is If, The contrapositive of the conditional statement is If not, The inverse of the conditional statement is If not, Interactive Questions on Converse Statement, if \(\begin{align} p \rightarrow q,\end{align}\) then, \(\begin{align} q \rightarrow p\end{align}\), if \(\begin{align} p \rightarrow q,\end{align}\) then, \(\begin{align} \sim{p} \rightarrow \sim{q}\end{align}\), if \(\begin{align} p \rightarrow q,\end{align}\) then, \(\begin{align} \sim{q} \rightarrow \sim{p}\end{align}\), if \(\begin{align} p \rightarrow q,\end{align}\) then, \(\begin{align} q \rightarrow p\end{align}\). The following theorem gives two important logical equivalencies. It will help to look at an example. https://www.thoughtco.com/converse-contrapositive-and-inverse-3126458 (accessed March 4, 2023). ," we can create three related statements: A conditional statement consists of two parts, a hypothesis in the if clause and a conclusion in the then clause. Okay, so a proof by contraposition, which is sometimes called a proof by contrapositive, flips the script. var vidDefer = document.getElementsByTagName('iframe'); NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions Class 11 Business Studies, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 8 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions For Class 6 Social Science, CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, Use of If and Then Statements in Mathematical Reasoning, Difference Between Correlation And Regression, CBSE Previous Year Question Papers Class 12 Maths, CBSE Previous Year Question Papers Class 10 Maths, ICSE Previous Year Question Papers Class 10, ISC Previous Year Question Papers Class 12 Maths, JEE Main 2023 Question Papers with Answers, JEE Main 2022 Question Papers with Answers, JEE Advanced 2022 Question Paper with Answers. A conditional statement defines that if the hypothesis is true then the conclusion is true. We will examine this idea in a more abstract setting. A contradiction is an assertion of Propositional Logic that is false in all situations; that is, it is false for all possible values of its variables. window.onload = init; 2023 Calcworkshop LLC / Privacy Policy / Terms of Service. 1: Modus Tollens for Inverse and Converse The inverse and converse of a conditional are equivalent. Now I want to draw your attention to the critical word or in the claim above. And then the country positive would be to the universe and the convert the same time. What is Symbolic Logic? - Conditional statement If it is not a holiday, then I will not wake up late. If there is no accomodation in the hotel, then we are not going on a vacation. Determine if each resulting statement is true or false. four minutes Example 1.6.2. The inverse of the given statement is obtained by taking the negation of components of the statement. Again, just because it did not rain does not mean that the sidewalk is not wet. Here are a few activities for you to practice. The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain." If the statement is true, then the contrapositive is also logically true. Take a Tour and find out how a membership can take the struggle out of learning math. There are two forms of an indirect proof. "If they cancel school, then it rains. 50 seconds Find the converse, inverse, and contrapositive of conditional statements. Starting with an original statement, we end up with three new conditional statements that are named the converse, the contrapositive, and the inverse. For. What we want to achieve in this lesson is to be familiar with the fundamental rules on how to convert or rewrite a conditional statement into its converse, inverse, and contrapositive. "&" (conjunction), "" or the lower-case letter "v" (disjunction), "" or In mathematics or elsewhere, it doesnt take long to run into something of the form If P then Q. Conditional statements are indeed important. Converse, Inverse, and Contrapositive: Lesson (Basic Geometry Concepts) Example 2.12. \(\displaystyle \neg p \rightarrow \neg q\), \(\displaystyle \neg q \rightarrow \neg p\). (Examples #1-3), Equivalence Laws for Conditional and Biconditional Statements, Use De Morgans 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), What is predicate logic? Related calculator: Not every function has an inverse. If it does not rain, then they do not cancel school., To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. What is a Tautology? "If Cliff is thirsty, then she drinks water"is a condition. That means, any of these statements could be mathematically incorrect. When youre given a conditional statement {\color{blue}p} \to {\color{red}q}, the inverse statement is created by negating both the hypothesis and conclusion of the original conditional statement. What are the properties of biconditional statements and the six propositional logic sentences? (virtual server 85.07, domain fee 28.80), hence the Paypal donation link. Solution We use the contrapositive that states that function f is a one to one function if the following is true: if f(x 1) = f(x 2) then x 1 = x 2 We start with f(x 1) = f(x 2) which gives a x 1 + b = a x 2 + b Simplify to obtain a ( x 1 - x 2) = 0 Since a 0 the only condition for the above to be satisfied is to have x 1 - x 2 = 0 which . - Inverse statement It is easy to understand how to form a contrapositive statement when one knows about the inverse statement. Every statement in logic is either true or false. If a number is a multiple of 4, then the number is a multiple of 8. English words "not", "and" and "or" will be accepted, too. There are 3 methods for finding the inverse of a function: algebraic method, graphical method, and numerical method. The contrapositive If the sidewalk is not wet, then it did not rain last night is a true statement. Here are some of the important findings regarding the table above: Introduction to Truth Tables, Statements, and Logical Connectives, Truth Tables of Five (5) Common Logical Connectives or Operators. half an hour. Because trying to prove an or statement is extremely tricky, therefore, when we use contraposition, we negate the or statement and apply De Morgans law, which turns the or into an and which made our proof-job easier! On the other hand, the conclusion of the conditional statement \large{\color{red}p} becomes the hypothesis of the converse. Then w change the sign. Okay. Eliminate conditionals If a number is not a multiple of 4, then the number is not a multiple of 8. Negations are commonly denoted with a tilde ~. We say that these two statements are logically equivalent. Note that an implication and it contrapositive are logically equivalent. Canonical DNF (CDNF) Still wondering if CalcWorkshop is right for you? Assuming that a conditional and its converse are equivalent. You may use all other letters of the English We start with the conditional statement If P then Q., We will see how these statements work with an example. Prove by contrapositive: if x is irrational, then x is irrational. Given statement is -If you study well then you will pass the exam. A statement obtained by negating the hypothesis and conclusion of a conditional statement. Notice, the hypothesis \large{\color{blue}p} of the conditional statement becomes the conclusion of the converse. Then show that this assumption is a contradiction, thus proving the original statement to be true. Now we can define the converse, the contrapositive and the inverse of a conditional statement. Contrapositive and converse are specific separate statements composed from a given statement with if-then. Therefore, the converse is the implication {\color{red}q} \to {\color{blue}p}. Mixing up a conditional and its converse. Taylor, Courtney. In the above example, since the hypothesis and conclusion are equivalent, all four statements are true. 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). In this mini-lesson, we will learn about the converse statement, how inverse and contrapositive are obtained from a conditional statement, converse statement definition, converse statement geometry, and converse statement symbol. But first, we need to review what a conditional statement is because it is the foundation or precursor of the three related sentences that we are going to discuss in this lesson. A rewording of the contrapositive given states the following: G has matching M' that is not a maximum matching of G iff there exists an M-augmenting path. Connectives must be entered as the strings "" or "~" (negation), "" or Find the converse, inverse, and contrapositive. Remember, we know from our study of equivalence that the conditional statement of if p then q has the same truth value of if not q then not p. Therefore, a proof by contraposition says, lets assume not q is true and lets prove not p. And consequently, if we can show not q then not p to be true, then the statement if p then q must be true also as noted by the State University of New York. Therefore: q p = "if n 3 + 2 n + 1 is even then n is odd. The inverse of a function f is a function f^(-1) such that, for all x in the domain of f, f^(-1)(f(x)) = x. Learn how to find the converse, inverse, contrapositive, and biconditional given a conditional statement in this free math video tutorial by Mario's Math Tutoring. If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below. In other words, contrapositive statements can be obtained by adding not to both component statements and changing the order for the given conditional statements. The converse statement for If a number n is even, then n2 is even is If a number n2 is even, then n is even. contrapositive of the claim and see whether that version seems easier to prove. Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step Given a conditional statement, we can create related sentences namely: converse, inverse, and contrapositive. To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. Textual expression tree What is the inverse of a function? For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining." Note: As in the example, the contrapositive of any true proposition is also true. 2) Assume that the opposite or negation of the original statement is true. Your Mobile number and Email id will not be published. not B \rightarrow not A. whenever you are given an or statement, you will always use proof by contraposition. If two angles have the same measure, then they are congruent. So change org. Courtney K. Taylor, Ph.D., is a professor of mathematics at Anderson University and the author of "An Introduction to Abstract Algebra.". The converse If the sidewalk is wet, then it rained last night is not necessarily true. If \(m\) is an odd number, then it is a prime number. (If p then q), Contrapositive statement is "If we are not going on a vacation, then there is no accomodation in the hotel." exercise 3.4.6. Operating the Logic server currently costs about 113.88 per year is the hypothesis. Together, we will work through countless examples of proofs by contrapositive and contradiction, including showing that the square root of 2 is irrational! Converse, Inverse, and Contrapositive. Given an if-then statement "if Be it worksheets, online classes, doubt sessions, or any other form of relation, its the logical thinking and smart learning approach that we, at Cuemath, believe in. Canonical CNF (CCNF) Assume the hypothesis is true and the conclusion to be false. For a given conditional statement {\color{blue}p} \to {\color{red}q}, we can write the converse statement by interchanging or swapping the roles of the hypothesis and conclusion of the original conditional statement. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Do my homework now . (If q then p), Inverse statement is "If you do not win the race then you will not get a prize." This follows from the original statement! The calculator will try to simplify/minify the given boolean expression, with steps when possible. If two angles are not congruent, then they do not have the same measure. Unicode characters "", "", "", "" and "" require JavaScript to be Graphical alpha tree (Peirce) The converse of disjunction. Legal. The steps for proof by contradiction are as follows: It may sound confusing, but its quite straightforward. The differences between Contrapositive and Converse statements are tabulated below. Dont worry, they mean the same thing. If the converse is true, then the inverse is also logically true. The contrapositive of the conditional statement is "If the sidewalk is not wet, then it did not rain last night." The inverse of the conditional statement is "If it did not rain last night, then the sidewalk is not wet." Logical Equivalence We may wonder why it is important to form these other conditional statements from our initial one. function init() { "What Are the Converse, Contrapositive, and Inverse?" Applies commutative law, distributive law, dominant (null, annulment) law, identity law, negation law, double negation (involution) law, idempotent law, complement law, absorption law, redundancy law, de Morgan's theorem. To save time, I have combined all the truth tables of a conditional statement, and its converse, inverse, and contrapositive into a single table. ThoughtCo, Aug. 27, 2020, thoughtco.com/converse-contrapositive-and-inverse-3126458. For example,"If Cliff is thirsty, then she drinks water." 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), Which of the following is a proposition? (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). Supports all basic logic operators: negation (complement), and (conjunction), or (disjunction), nand (Sheffer stroke), nor (Peirce's arrow), xor (exclusive disjunction), implication, converse of implication, nonimplication (abjunction), converse nonimplication, xnor (exclusive nor, equivalence, biconditional), tautology (T), and contradiction (F). How do we show propositional Equivalence? alphabet as propositional variables with upper-case letters being We may wonder why it is important to form these other conditional statements from our initial one. Hope you enjoyed learning! Instead of assuming the hypothesis to be true and the proving that the conclusion is also true, we instead, assumes that the conclusion to be false and prove that the hypothesis is also false. 6 Another example Here's another claim where proof by contrapositive is helpful. Contrapositive is used when an implication has many hypotheses or when the hypothesis specifies infinitely many objects. 30 seconds Atomic negations The symbol ~\color{blue}p is read as not p while ~\color{red}q is read as not q . is the conclusion. } } } Contrapositive. The inverse of To calculate the inverse of a function, swap the x and y variables then solve for y in terms of x. The steps for proof by contradiction are as follows: Assume the hypothesis is true and the conclusion to be false. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining." Note: As in the example, the contrapositive of any true proposition is also true. vidDefer[i].setAttribute('src',vidDefer[i].getAttribute('data-src')); A converse statement is the opposite of a conditional statement. A biconditional is written as p q and is translated as " p if and only if q . Similarly, if P is false, its negation not P is true. S For example, consider the statement. Definition: Contrapositive q p Theorem 2.3. A conditional statement is a statement in the form of "if p then q,"where 'p' and 'q' are called a hypothesis and conclusion. Sometimes you may encounter (from other textbooks or resources) the words antecedent for the hypothesis and consequent for the conclusion. Mathwords: Contrapositive Contrapositive Switching the hypothesis and conclusion of a conditional statement and negating both. ThoughtCo. Disjunctive normal form (DNF) First, form the inverse statement, then interchange the hypothesis and the conclusion to write the conditional statements contrapositive. represents the negation or inverse statement. It will also find the disjunctive normal form (DNF), conjunctive normal form (CNF), and negation normal form (NNF). 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? Maggie, this is a contra positive. Truth Table Calculator. So instead of writing not P we can write ~P. - Conditional statement, If you do not read books, then you will not gain knowledge. The contrapositive of a conditional statement is a combination of the converse and the inverse. is The calculator will try to simplify/minify the given boolean expression, with steps when possible. What we see from this example (and what can be proved mathematically) is that a conditional statement has the same truth value as its contrapositive. There . -Inverse statement, If I am not waking up late, then it is not a holiday. "What Are the Converse, Contrapositive, and Inverse?" We also see that a conditional statement is not logically equivalent to its converse and inverse. What are the types of propositions, mood, and steps for diagraming categorical syllogism? Optimize expression (symbolically) To calculate the inverse of a function, swap the x and y variables then solve for y in terms of x. is A These are the two, and only two, definitive relationships that we can be sure of. But this will not always be the case! To form the converse of the conditional statement, interchange the hypothesis and the conclusion. The contrapositive of the conditional statement is "If not Q then not P." The inverse of the conditional statement is "If not P then not Q." if p q, p q, then, q p q p For example, If it is a holiday, then I will wake up late. AtCuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students! Required fields are marked *. A contrapositive statement changes "if not p then not q" to "if not q to then, notp.", If it is a holiday, then I will wake up late. In other words, to find the contrapositive, we first find the inverse of the given conditional statement then swap the roles of the hypothesis and conclusion. As you can see, its much easier to assume that something does equal a specific value than trying to show that it doesnt. with Examples #1-9. Example Also, since this is an "iff" statement, it is a biconditional statement, so the order of the statements can be flipped around when . Let's look at some examples. A statement obtained by reversing the hypothesis and conclusion of a conditional statement is called a converse statement. 1: Common Mistakes Mixing up a conditional and its converse. This is aconditional statement. Textual alpha tree (Peirce) "It rains" Write the contrapositive and converse of the statement. A conditional statement takes the form If p, then q where p is the hypothesis while q is the conclusion. Instead, it suffices to show that all the alternatives are false. - Conditional statement, If you are healthy, then you eat a lot of vegetables. Then show that this assumption is a contradiction, thus proving the original statement to be true.
