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
$B \rightarrow( A \vee C )$
$(\sim B ) \wedge( A \wedge C )$
$B \rightarrow((\sim A ) \vee(\sim C ))$
$B \rightarrow( A \wedge C )$
Which of the following is true
The statement $p → (p \leftrightarrow q)$ is logically equivalent to :-
The proposition $\left( { \sim p} \right) \vee \left( {p\, \wedge \sim q} \right)$
$\left( { \sim \left( {p \vee q} \right)} \right) \vee \left( { \sim p \wedge q} \right)$ is logically equivalent to
$\sim (p \vee q) \vee (\sim p \wedge q)$ is logically equivalent to