$(p \wedge \sim q) \wedge (\sim p \vee q)$ is :-

If $p \Rightarrow (\sim p \vee q)$ is false,the truth values of $p$ and $q$ are respectively

Given below are two pairs of statements. Combine these two statements using "if and only if".
$p:$ If the sum of digits of a number is divisible by $3,$ then the number is divisible by $3.$
$q:$ If a number is divisible by $3,$ then the sum of its digits is divisible by $3.$

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

The converse of the contrapositive of the conditional $p \rightarrow \sim q$ is

Let the operations $*, \odot \in \{\wedge, \vee\}$. If $(p * q) \odot (p \odot \sim q)$ is a tautology,then the ordered pair $(*, \odot)$ is: