If $p \Rightarrow (q \vee r)$ is false, then the truth values of $p, q, r$ are respectively

  • A

    $T, F, F$

  • B

    $F, F, F$

  • C

    $F, T, T$

  • D

    $T, T, F$

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Consider the following two propositions:

$P_1: \sim( p \rightarrow \sim q )$

$P_2:( p \wedge \sim q ) \wedge((\sim p ) \vee q )$

If the proposition $p \rightarrow((\sim p ) \vee q )$ is evaluated as $FALSE$, then

  • [JEE MAIN 2022]

The negation of the compound statement $^ \sim p \vee \left( {p \vee \left( {^ \sim q} \right)} \right)$ is