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

  • A

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

  • B

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

  • C

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

  • D

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

Similar Questions

$(p\rightarrow q) \leftrightarrow (q \vee  ~ p)$ is

The logical statement $(p \Rightarrow q){\wedge}(q \Rightarrow \sim p)$ is equivalent to

  • [JEE MAIN 2020]

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

  • [JEE MAIN 2021]

Negation of the Boolean expression $p \Leftrightarrow( q \Rightarrow p )$ is.

  • [JEE MAIN 2022]

Which of the following is always true