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

$\sim(P \vee Q) \rightarrow \sim R$

JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

1 Easy

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Analyzing +4 | -1

If the truth value of the statement

(P \wedge(\sim R)) \rightarrow

((\sim R) \wedge Q)

F

, then the truth value of which of the following is

F

View answer and explanation

Correct option: D

\sim(R \vee Q) \rightarrow \sim P

Option D (

\sim(R \vee Q) \rightarrow \sim P

) is correct because when the given statement is false, P is true, R is false, and Q is false, making this option also false.

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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