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?

Correct answer: (C) IfS_2 is False, then S_1 is True. S_1:~p∨q∨~p∨r ≡~p∨q∨r S_2:p→q∨r≡~p∨q∨r So S_1 is equivalent to S_2

Q50 / 90 · JEE Main 2022 (28 Jun Shift 1) · Mathematics

Let $p, q, r$ be three logical statements. Consider the compound statements
$S_{1} : ((~ p) \lor q) \lor ((~ p) \lor r)$ and $S_{2} : p \to (q \lor r)$
Then, which of the following is NOT true?

$S_{1} : (~ p \lor q) \lor (~ p \lor r)$

$\equiv ~ p \lor (q \lor r)$

$S_{2} : p \to (q \lor r)$ $\equiv ~ p \lor (q \lor r)$

So $S_{1}$ is equivalent to $S_{2}$

Hence, the correct answer is option: 'C'.