The Boolean expression $(p \wedge \sim q) \Rightarrow(q \vee \sim p)$ is equivalent to :

(A) $\mathrm{q} \Rightarrow \mathrm{p}$

(B) $\sim \mathrm{q} \Rightarrow \mathrm{p}$

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Mathematical Reasoning *

The Boolean expression

(p \land \sim q) \Rightarrow (q \lor \sim p)

is equivalent to :

Answer: (C)

Replacing the implication by a disjunction through

A \Rightarrow B \equiv \sim A \lor B

(p \land \sim q) \Rightarrow (q \lor \sim p) \equiv \sim (p \land \sim q) \lor (q \lor \sim p) \equiv (\sim p \lor q) \lor (q \lor \sim p)

The two brackets are the same pair of literals repeated, and a disjunction absorbs its own repeats, so the whole expression reduces to

\sim p \lor q

. That disjunction is precisely the implication

p \Rightarrow q

JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Single correct option