If $\left( {p \wedge  \sim q} \right) \wedge \left( {p \wedge r} \right) \to  \sim p \vee q$ is false, then the truth values of $p, q$ and $r$ are respectively

Consider the following two propositions:

$P_1: \sim( p \rightarrow \sim q )$

$P_2:( p \wedge \sim q ) \wedge((\sim p ) \vee q )$

If the proposition $p \rightarrow((\sim p ) \vee q )$ is evaluated as $FALSE$, then

Negation of the conditional : “If it rains, I shall go to school” is

The following statement $\left( {p \to q} \right) \to $ $[(\sim p\rightarrow q) \rightarrow  q ]$ 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

Suppose $p, q, r$ are positive rational numbers such that $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is also rational. Then