The proposition $p \to \sim \left( {p \wedge \sim q} \right)$ is

Either a tautology or a contradiction

JEE MATHEMATICS MCQ: MATHEMATICAL REASONING

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The proposition

p \to \sim \left( {p \wedge \sim q} \right)

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Correct option: D

Neither a tautology nor a contradiction

The proposition is neither a tautology nor a contradiction because it simplifies to

\sim p \vee q

, which depends on the truth values of both p and q.

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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