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Validation of Statement

If p → p ∧∼ q...

Question

If $p \to (p \land \sim q)$ is false. Then the truth values of $p$ and $q$ are respectively

F, T

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T, F

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F, F

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T, T

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Solution

The correct option is D $T, T$
$p \to (p \land \sim q)$
Truth table:
$\begin{matrix} p & q & \sim q & (p \land \sim q) & p \to (p \land \sim q) T & T & F & F & F T & F & T & T & T F & T & F & F & T F & F & T & F & T \end{matrix}$
$p \to (p \land \sim q)$ is false when $p$ is true and $q$ is true.

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