Negation of $p \wedge (\sim q \vee \sim r)$ is -

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

If $(p\; \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false, then $p$ 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

$(i)$ $p \leftrightarrow  q$ 

$(ii)$ $~ p \leftrightarrow q$

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

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

If $p$ and $q$ are simple propositions, then $p \Rightarrow q$ is false when

The negation of the statement $(( A \wedge( B \vee C )) \Rightarrow( A \vee B )) \Rightarrow A$ is