Consider the following statements:

$P$ : I have fever

$Q:$ I will not take medicine

$R$ : I will take rest

The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to:

  • [JEE MAIN 2023]
  • A

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

  • B

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

  • C

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

  • D

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

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The proposition $ \sim \left( {p\,\vee \sim q} \right) \vee  \sim \left( {p\, \vee q} \right)$ is logically equivalent to

  • [JEE MAIN 2014]