The number of choices for $\Delta \in \left\{\wedge ,\vee ,\Rightarrow ,\iff \right\}$, such that $\left(p\Delta q\right)\Rightarrow \left(\left(p\Delta ~q\right)\vee \left(\left(~p\right)\Delta q\right)\right)$ is a tautology, is

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

Consider the following two propositions :
$P_1$: $~\left(p\to ~q\right)$
$P_2$: $\left(p\wedge ~q\right)\wedge \left(\left(~p\right)\vee q\right)$

If the proposition $p\to \left(\left(~p\right)\vee q\right)$ is evaluated as FALSE, then

Let $p,q,r$ be three logical statements. Consider the compound statements
$S_1:\left(\left(~p\right)\vee q\right)\vee \left(\left(~p\right)\vee r\right)$ and $S_2:p\to \left(q\vee r\right)$
Then, which of the following is NOT true?