Which of the following statements is a tautology?

$\sim (p \Rightarrow q) \Leftrightarrow \sim p\; \vee \sim q$ is

For the statements $p$ and $q$, consider the following compound statements :

$(a)$ $(\sim q \wedge( p \rightarrow q )) \rightarrow \sim p$

$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$

Then which of the following statements is correct?

The propositions $(p \Rightarrow \;\sim p) \wedge (\sim p \Rightarrow p)$ is a

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

Contrapositive of the statement:

'If a function $f$ is differentiable at $a$, then it is also continuous at $a$', is