The compound statement $(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) \Rightarrow((\sim P ) \wedge(\sim Q ))$ is equivalent to

  • [JEE MAIN 2023]
  • A

    $((\sim P ) \vee Q ) \wedge((\sim Q ) \vee P )$

  • B

    $(\sim Q) \vee P$

  • C

    $((\sim P ) \vee Q ) \wedge(\sim Q )$

  • D

    $(\sim P ) \vee Q$

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The negation of the Boolean expression $ \sim \,s\, \vee \,\left( { \sim \,r\, \wedge \,s} \right)$ is equivalent to

  • [JEE MAIN 2019]

The negation of $ \sim s \vee \left( { \sim r \wedge s} \right)$ is equivalent to