$\sim (p \vee q) \vee (~ p \wedge q)$ is logically equivalent to

$\sim (p \Leftrightarrow q)$ is

The number of values of $r \in\{p, q, \sim p , \sim q \}$ for which $((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)$ is a tautology, is:

Let $p$ and $q $ stand for the statement $"2 × 4 = 8" $ and $"4$ divides $7"$ respectively. Then the truth value of following biconditional statements

$(i)$ $p \leftrightarrow  q$ 

$(ii)$ $~ p \leftrightarrow q$

$(iii)$ $~ q \leftrightarrow p$

$(iv)$ $~ p \leftrightarrow ~ q$

Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”

The negation of the compound proposition $p \vee (\sim p \vee q)$ is