State the converse, inverse and contrapositive of the following proposition, stating it as a conditional.

A parallelogram which is inscribed in a circle is a rectangle.

State the converse, inverse and contrapositive of the following proposition, stating it as a conditional.

The ground being wet, there has been rainfall at night.

Are the following pair of statements negation of each other?

The number $\pi$ is not a rational number.

The number $\pi$ is not an irrational number.

Are the following pair of statements negation of each other?

The number $\pi$ is a rational number.

The number $\pi$ is an irrational number.

Write the component statements for the compound statement and check whether the compound statement is true or false.

$24$ is a multiple of $4$ and $6$.

Write the component statement of the compound statement and check whether the compound statement is true or false.

The school is closed if there is a holiday or a Sunday.

Write the component statement of the following compound statements and check whether the compound statement is true or false.

$7$ is an rational number or an irrational number.

Write the component statements for the compound statement and check whether the compound statement is true or false.

$57$ is divisible by $2$ or $3$

Write the component statements for the compound statement and check whether the compound statement is true or false.

All living things have two eyes and two legs.