The contrapositive of the converse of $p \Rightarrow q$ is......

For each of the following compound statements,first identify the corresponding component statements. Then check whether the statements are true or not.
If $a$ and $b$ are integers,then $ab$ is a rational number.

The statement $(p \wedge \sim q) \wedge (\sim p \vee q)$ is which of the following?

If $p :$ It is raining today.
$q :$ $I$ go to school.
$r :$ $I$ will meet my friends.
$s :$ $I$ will go to watch a movie.
Then write the statement: 'If it does not rain today or $I$ do not go to school,then $I$ will meet my friends and go to watch a movie' in symbolic form.

State the converse and contrapositive of the following statement:
$p:$ $A$ positive integer is prime only if it has no divisors other than $1$ and itself.

$\sim ((\sim p) \wedge q)$ is equivalent to