Let $p, q, r$ be three statements such that the truth value of $\sim(\sim p \vee \sim q) \rightarrow(\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively:

JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

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Analyzing +4 | -1

Let

p, q, r

be three statements such that the truth value of

\sim(\sim p \vee \sim q) \rightarrow(\sim q \vee r)

F

. Then the truth values of

p, q, r

are respectively:

View answer and explanation

Correct option: D

T, T, F

The correct answer is D (T, T, F) because when p and q are true and r is false, the given expression evaluates to false, satisfying the condition.

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p:A

q:A

\sqrt{3}

p

q

p \rightarrow q

{F_1}(A,\,B,\,C) = \left( {A \wedge \sim B} \right) \vee \left[ { \sim C \wedge \left( {A \vee B} \right)} \right] \vee \sim A

{F_2}(A,\,B) = \left( {A \vee B} \right) \vee (B \to \, \sim \,A)

p

n

q:

n

p \Leftrightarrow q