Answer to Question #262157 in Discrete Mathematics for Amit

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. Taking into account that the implication $s\to r$ is false if and only if $s$ is true and $r$ is false, we conclude that $q$ is true and $\sim p$ is false. It follows that $p$ is true and $\sim q$ is false. Therefore, we get that the truth value of $p\to\sim q$ is false.