For the circuit shown below,the Boolean polynomial is

$p$: 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 $V_1$ and $V_2$ are the respective truth values of the contrapositive of $p$ and $q$,then $(V_1, V_2) \equiv$

Write the component statements of the following compound statement and check whether the compound statement is true or false.
$A$ line is straight and extends indefinitely in both directions.

Which of the following statements is correct?
$(a)$ $S_1: (p \wedge q) \equiv \sim(p \rightarrow \sim q)$
$(b)$ $S_2: (p \wedge q) \wedge (\sim p \vee \sim q)$ is a tautology
$(c)$ $S_3: [p \wedge (p$ $\rightarrow \sim q)]$ $\rightarrow q$ is a contradiction
$(d)$ $S_4: p$ $\rightarrow (q$ $\rightarrow p)$ is a contingency

The contrapositive of the statement "$I$ go to school if it does not rain" is

The statement $(p \wedge (\sim q)) \vee ((\sim p) \wedge q) \vee ((\sim p) \wedge (\sim q))$ is equivalent to