QJEEM22Maeec5: JEE Main 2022 Mathematics - Class 11 JEEM22Maeec5 Solution: Consider the following two propositions: If the proposition is…

Question

Verified Solution • 2025–26 Session moderate

Consider the following two propositions:

$P1: \sim (p \to \sim q)$

$P2:(p \wedge \sim q) \wedge (( \sim p) \vee q)$

If the proposition $p \to (( \sim p) \vee q)$ is evaluated as FALSE, then :

Accepted Answer

Given

p \rightarrow(\sim p \vee q)

is false

\Rightarrow \sim p \vee q

is false and

p

is true

Now

p=

True.

\sim T \vee q=F

F \vee q=F \Rightarrow q

is false

P 1: \sim(T \rightarrow \sim F) \equiv \sim(T \rightarrow T) \equiv

False.

\begin{aligned}P 2:(T \wedge \sim F) \wedge(\sim T \vee F) &amp; \equiv(T \wedge T) \wedge(F \vee F) \\\\&amp; \equiv T \wedge F \equiv \text { False }\end{aligned}

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