The Boolean expression $\left(\sim\left(p^{\wedge} q\right)\right) \vee q$ is equivalent to

  • [JEE MAIN 2022]
  • A

    $q \rightarrow\left(p^{\wedge} q\right)$

  • B

    $p \rightarrow q$

  • C

    $p \rightarrow(p \vee q)$

  • D

    $p \rightarrow(p \rightarrow q)$

Similar Questions

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]

$(p \to q) \leftrightarrow (q\ \vee  \sim p)$ is 

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

  • [JEE MAIN 2017]

Let $p, q, r$ denote arbitrary statements. Then the logically equivalent of the statement $p\Rightarrow (q\vee r)$ is

  • [JEE MAIN 2014]

Which of the following is logically equivalent to $\sim(\sim p \Rightarrow q)$