Which of the following pairs are not logically equivalent ?

  • A

    $ \sim \left( { \sim p} \right)$ and $p$

  • B

    $p\, \vee \,\left( {p\, \wedge \,q} \right)$ and $q$

  • C

    $ \sim \,\left( {p\, \wedge \,q} \right)$ and $\left( { \sim p} \right)\, \vee \,\left( { \sim q} \right)$

  • D

    $ \sim \left( { \sim p\, \wedge \,q} \right)$ and $\left( {p\, \vee \, \sim \,q} \right)$ 

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Which of the following is not a statement

$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$ is equivalent to $(\sim p)$ when $r$ is.

  • [JEE MAIN 2022]