Write the converse and contra positive statements of the statement "$x$ is an even number implies that $x$ is divisible by $4$.

Toolbox:
• Converse of if $p$ then $q$ is If $q$ then $p$.
• Contra positive of If $p$ then $q$ is If ~$q$ then ~$p$.
The given statement is:
$x$ is an even number implies that $x$ is divisible by $4$.
This statement can be written as
If $x$ is an even number then $x$ is divisible by $4$.
Here $p\rightarrow$ $x$ is an even number.
$q\rightarrow$ $x$ is divisible by $4$
~$p\rightarrow$ $x$ is not an even number.
~$q\rightarrow$ $x$ is not divisible by $4$.
$\therefore$ The converse of the given statement is
If $x$ is divisible by $4$ then $x$ is an even number.
The contra positive statement is
If $x$ is not divisible by $4$ then $x$ is not an even number.