Thus, there are integers k and m for which x = 2k and y . Claim 11 For any integers a and b, a+b 15 implies that a 8 or b 8. In mathematics, we observe many statements with if-then frequently. Therefore, the contrapositive of the conditional statement {\color{blue}p} \to {\color{red}q} is the implication ~\color{red}q \to ~\color{blue}p. Now that we know how to symbolically write the converse, inverse, and contrapositive of a given conditional statement, it is time to state some interesting facts about these logical statements. Still wondering if CalcWorkshop is right for you? To get the converse of a conditional statement, interchange the places of hypothesis and conclusion. Now I want to draw your attention to the critical word or in the claim above. (P1 and not P2) or (not P3 and not P4) or (P5 and P6). If the conditional is true then the contrapositive is true. Example #1 It may sound confusing, but it's quite straightforward. Converse, Inverse, and Contrapositive Examples (Video) The contrapositive is logically equivalent to the original statement. 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. Jenn, Founder Calcworkshop, 15+ Years Experience (Licensed & Certified Teacher). We will examine this idea in a more abstract setting. Okay. 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. It will also find the disjunctive normal form (DNF), conjunctive normal form (CNF), and negation normal form (NNF). For example,"If Cliff is thirsty, then she drinks water." Do It Faster, Learn It Better. 6 Another example Here's another claim where proof by contrapositive is helpful.
What is contrapositive in mathematical reasoning? For more details on syntax, refer to
This video is part of a Discrete Math course taught at the University of Cinc. Again, just because it did not rain does not mean that the sidewalk is not wet. Taylor, Courtney. Then show that this assumption is a contradiction, thus proving the original statement to be true. An example will help to make sense of this new terminology and notation. for (var i=0; i