Write the following statement in the form "if-then":
$A$ quadrilateral is a parallelogram if its diagonals bisect each other.

Verify by the method of contradiction.
$p: \sqrt{7}$ is irrational

Let,$p$: Ramesh listens to music.
$q$: Ramesh is out of his village.
$r$: It is Sunday.
$s$: It is Saturday.
Then the statement "Ramesh listens to music only if he is in his village and it is Sunday or Saturday" can be expressed as:

Consider the following statements:
$p$: the switch $S_1$ is closed.
$q$: the switch $S_2$ is closed.
$r$: the switch $S_3$ is closed.
Then the switching circuit represented by the statement $(p \wedge q) \vee (\sim p \wedge (\sim q \vee p \vee r))$ is

The converse of the statement "If $p < q$,then $p - x < q - x$" is -

The Boolean expression $\sim(p \vee q) \vee (\sim p \wedge q)$ is equivalent to: