Consider the following statements :

$A$ : Rishi is a judge.

$B$ : Rishi is honest.

$C$ : Rishi is not arrogant.

The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is

  • [JEE MAIN 2022]
  • A

    $B \rightarrow( A \vee C )$

  • B

    $(\sim B ) \wedge( A \wedge C )$

  • C

    $B \rightarrow((\sim A ) \vee(\sim C ))$

  • D

    $B \rightarrow( A \wedge C )$

Similar Questions

Which of the following is true

The statement $p → (p \leftrightarrow  q)$ is logically equivalent to :-

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

  • [JEE MAIN 2017]

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

$\sim (p \vee q) \vee (\sim p \wedge q)$ is logically equivalent to