Question

Let$p,q,r$ be three logical statements. Consider the compound statements
$S_1:\left(\right(\sim p)\vee q)\vee \left(\right(\sim p)\vee r)$ and
$S_2:p\to (q\vee r)$
Then, which of the following is NOT true?

• A. If $S_2$ is False, then $S_1$ is True
• B. If $S_2$ is True, then $S_1$ is True
• C. If $S_2$ is False, then $S_1$ is False
• D. If $S_1$ is False, then $S_2$ is False

Answer 1

The correct option is A

If $S_2$ is False, then $S_1$ is True

$S_1:(\sim p\vee q)\vee (\sim p\vee r)$

$\cong (\sim p\vee q\vee r)$

$S_2:p\to (q\vee r)$ is logically equivalent to $(\sim p\vee (q\vee r)$

So, option (C) is incorrect.