Let p and q be two statements. Then ~(p∧(p→~q) is equivalent to

Correct answer: (C) ~p∨q. Given, ~(p∧(p→~q) ≡~p∨~(~p∨~q) as A→B≡~A∨B ≡~p∨(p∧q) as ~A∨B≡~A∧~B ≡(~p∨p)∧(~p∨q) ≡t∧(~p∨q) ≡~p∨q ≡(~p)∨q

Q45 / 90 · JEE Main 2023 (24 Jan Shift 2) · Mathematics

Let $p$ and $q$ be two statements. Then $~ (p \land (p \to ~ q)$ is equivalent to

Given,

$~ (p \land (p \to ~ q)$

$\equiv ~ p \lor ~ (~ p \lor ~ q)$ $\{as A \to B \equiv ~ A \lor B\}$

$\equiv ~ p \lor (p \land q)$ $\{as ~ (A \lor B) \equiv ~ A \land ~ B\}$

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

$\equiv t \land (~ p \lor q)$

$\equiv ~ p \lor q$

$\equiv (~ p) \lor q$

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