If the statement $(p \vee \sim r) \rightarrow (q \wedge r)$ is false and the statement $q$ is true,then what is the truth value of statement $p$?

If the truth value of the statement $p \to (\sim q \vee r)$ is false $(F)$,then the truth values of the statements $p, q, r$ are respectively:

Which of the following sentences are statements? Give reasons for your answer.
The sum of $5$ and $7$ is greater than $10.$

Check whether the following statement is true or false by proving its contrapositive: If $x, y \in \mathbb{Z}$ such that $xy$ is odd,then both $x$ and $y$ are odd.

If $p: \text{A man is happy}$,$q: \text{A man is rich}$,then the symbolic form of '$\text{A man is neither happy nor rich}$' is

Consider the following two statements :
$P :$ If $7$ is an odd number,then $7$ is divisible by $2.$
$Q :$ If $7$ is a prime number,then $7$ is an odd number.
If $V_1$ is the truth value of the contrapositive of $P$ and $V_2$ is the truth value of the contrapositive of $Q,$ then the ordered pair $(V_1, V_2)$ equals