Answer to Question #108659 in Discrete Mathematics for Justin Lee

Question

Give four examples of implications and for each write down their contrapositive. Have two be real world examples and two be math examples.

Answer 1

Real world

1. If it rains then I will stay indoors. The contrapositive is, if I will not stay indoors then it does not rain.

2. If I pass my examination then I will proceed to the next class. The contrapositive is, if I do not proceed to the next class then I did not pass my examination.

Math examples

P and Q are statements

1. P$\implies$ Q

Contrapositive : $\neg Q\implies\neg P$

2. If n is even then 2n is even. The contrapositive is, if 2n is not even, then n is not even.