Question

Let $p, q, r$be three logical statements. Consider the compound statements
$S_1 : ((~p) ∨q) ∨ ((~p) ∨r)$ and
$S_2 :p→ (q∨r)$
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)

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

Answer 2

$S_1: (~p∨q) ∨ (~ p∨r)$
$S_1≅ (~ p∨q∨r)$
$S_2: ~p ∨ (q∨r)$
Both $S_1$ and $S_2$ are same

So, the correct option is (C): If $S_2$ is False, then $S_1$ is True.