The following statement $\left( {p \to q} \right) \to $ $[(\sim p\rightarrow q) \rightarrow  q ]$ 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

The false statement in the following is

For integers $m$ and $n$, both greater than $1$ , consider the following three statements
$P$ : $m$ divides $n$
$Q$ : $m$ divides $n^2$
$R$ : $m$ is prime,
then true statement  is

Which Venn diagram represent the truth of the statement“Some teenagers are not dreamers”

Let $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ be such that $(p \wedge q) \Delta((p \vee q) \Rightarrow q)$ is a tautology. Then $\Delta$ is equal to