Let $^{*}, \Delta \in\{\wedge, \mathrm{v}\}$ be such that the Boolean expression $(\mathrm{p}^{*} \sim \mathrm{q}) \Rightarrow (\mathrm{p} \Delta \sim \mathrm{q})$ is a tautology. Then :

(A) $^{*}=\wedge, \Delta=\vee$

(B) $^{*}=\wedge, \Delta=\wedge$

(C) $^{*}=\vee, \Delta=\wedge$

JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Mathematical Reasoning *

Let

^{*}, Δ \in {\land, v}

be such that the Boolean expression

(p^{*} \sim q) \Rightarrow (p Δ \sim q)

is a tautology. Then :

Answer: (A)

For the implication to be a tautology, the antecedent being true must force the consequent to be true. Taking the first connective as

\land

and the second as

\lor

: whenever

p \land \sim q

is true, both

p

and

\sim q

are true, so

p \lor \sim q

is true; and when the antecedent is false the implication holds automatically. Hence

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

is a tautology, so the first symbol is

\land

and the second is

\lor

JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Single correct option