QJEEM21Mac684: JEE Main 2021 Mathematics - Class 11 JEEM21Mac684 Solution: If P and Q are two statements, then which of the following…

LHS of all the options are same i.e.

$((P \to Q) \wedge \sim Q)$

$\equiv ( \sim P \vee Q) \wedge \sim Q$

$\equiv ( \sim P \wedge \sim Q) \vee (Q \wedge \sim Q)$

$\equiv \sim P \wedge \sim Q$

(A) $( \sim P \wedge \sim Q) \to Q$

$\equiv \sim ( \sim P \wedge \sim Q) \vee Q$

$\equiv (P \vee Q) \vee Q \ne$ Tautology

(B) $( \sim P \wedge \sim Q) \to P$

$\equiv \sim ( \sim P \wedge \sim Q) \vee \sim P$

$\equiv (P \vee Q) \vee \sim P$

(C) $( \sim P \wedge \sim Q) \to P$

$\equiv (P \wedge Q) \wedge P \ne$ Tautology

(D) $( \sim P \wedge \sim Q) \to (P \vee Q)$

$\equiv (P \wedge Q) \wedge (P \vee Q) \ne$ Tautology