Answer to Question #261899 in Discrete Mathematics for Arya

Question

Give the truth value.

P-~q,if q-~p is false

Answer 1

Let us give the truth value $p\to\sim q,$ if $q\to\sim p$ is false. Since the implication $A\to B$ is false if and only if $A$ is true and $B$ is false, we conclude that $q$ is true and $\sim p$ is false. It follows that $p$ is true and $\sim q$ is false. Consequently, we conclude that the truth value of $p\to\sim q$ is false.