Consider the following two propositions: P1 : \(\sim(\mathrm{p} \rightarrow \sim \mathrm{q})\) P2: \((\mathrm{p} \wedge \sim \mathrm{q}) \wedge((\sim \mathrm{p}) \vee \mathrm{q})\) If the proposition \(p \rightarrow((\sim p) \vee q)\) is evaluated as FALSE, then:

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Mathematical Reasoning *

Consider the following two propositions:
P1 :

\sim (p \to\sim q)

P2:

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

If the proposition

p \to ((\sim p) \lor q)

is evaluated as FALSE, then:

Answer: (C)

The proposition

p \to (\sim p \lor q)

is FALSE only when

p

is TRUE and

\sim p \lor q

is FALSE, which means

p

is TRUE and

q

is FALSE. For P1:

\sim (p \to\sim q) =\sim (T \to T) =\sim T = F

. For P2:

(p \land \sim q) \land (\sim p \lor q) = (T \land T) \land (F \lor F) = T \land F = F

. Thus both P1 and P2 are FALSE.

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Single correct option