Question

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

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

Answer 1

Answer: (C)

$s_1:(\sim p\vee q)\vee (\sim p\vee r)$
$\equiv \sim p\vee (q\vee r)$
$s_2:p\to (q\vee r)$
$\equiv \sim p\vee (q\vee r)\to$ By conditional law
$s_1\equiv s_2$