Are the following pairs of statements negations of each other:
$1$. The number $x$ is a rational number.
$2$. The number $x$ is an irrational number.

The negation of $(p$ $\Rightarrow q)$ $\Rightarrow (q$ $\Rightarrow p)$ is

For each of the following compound statements,first identify the connecting words and then break it into component statements.
The sand heats up quickly in the Sun and does not cool down fast at night.

Given the statement: "If you live in Delhi,then you have winter clothes."
Identify the following statements as contrapositive or converse of the given statement:
$(i)$ If you do not have winter clothes,then you do not live in Delhi.
$(ii)$ If you have winter clothes,then you live in Delhi.

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.

The contrapositive statement of the statement "If $x$ is a prime number,then $x$ is odd" is