QJEEM22Ma7cd2: JEE Main 2022 Mathematics - Class 11 JEEM22Ma7cd2 Solution: If the truth value of the statement ( P ∧ ( ∼ R ) ) → ( ( ∼ R ) …

Question

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If the truth value of the statement $(P \land (\sim R)) \to ((\sim R) \land Q)$ is F, then the truth value of which of the following is $F$ ?

Accepted Answer

\mathrm{X} \Rightarrow \mathrm{Y}

is a false

when

X

is true and

Y

is false

So,

\mathrm{P} \rightarrow \mathrm{T}, \mathrm{Q} \rightarrow \mathrm{F}, \mathrm{R} \rightarrow \mathrm{F}

(A)

\mathrm{P} \vee \mathrm{Q} \rightarrow \sim \mathrm{R}

is

\mathrm{T}

(B)

\mathrm{R} \vee \mathrm{Q} \rightarrow \sim \mathrm{P}

is

\mathrm{T}

(C)

\sim(\mathrm{P} \vee \mathrm{Q}) \rightarrow \sim \mathrm{R}

is

\mathrm{T}

(D)

\sim(\mathrm{R} \vee \mathrm{Q}) \rightarrow \sim \mathrm{P}

is

\mathrm{F}

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