The negative of the statement $ \sim \,p\, \wedge \,(p\, \vee q)\,$ is

JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

1 Easy

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Application +4 | -1

The negative of the statement

\sim \,p\, \wedge \,(p\, \vee q)\,

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Correct option: B

p\, \vee \sim q

Option B (

p\, \vee \sim q

) is the correct negative of the given statement, obtained using De Morgan's laws and logical equivalences.

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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