Answer to Question #290211 in Discrete Mathematics for dadan

Question

State the converse and contrapositive of each of the following implications.

(a) If it does not rain tonight, I will go fishing tomorrow.

(b) If it rains tonight, then I will stay at home.

Answer 1

Converse of implication $A\implies B$ is $B\implies A$

Contrapositive of implication $A\implies B$ is $\neg B\implies \neg A$

So,

a) The converse is: If I will go fishing tomorrow, then it does not rain today

The contrapositive is: If I will not go fishing tomorrow, then it does rain today

b) The converse is: If I will stay at home, then it is rains tonight

The contrapositive is: If I will not stay at home, then it is not rains tonight