Question

If $(p\wedge \sim r)\to (\sim p\vee q)$ is false, then the truth values of $p,q,r$ respectively, are

• A. T, F, T
• B. F, T, T
• C. F, F, T
• D. T, F, F

Answer 1

The correct option is D

T, F, F

$a\to b$ is false only when $a$ is true and $b$ is false.
Given $(p\wedge \sim r)\to (\sim p\vee q)$ is false.

$\Rightarrow (p\wedge \sim r)$ is T and $(\sim p\vee q)$ is F.

$\Rightarrow p$ is T, $\sim r$ is T and $\sim p$ is F, $q$ is F.

$\Rightarrow p$ is T, $r$ is F, $p$ is T, $q$ is F.