Write the contrapositive and converse of the statement: "If $x$ is prime then $x$ is odd."

Question

$\begin{array}{1 1} \text{Converse: If x is odd then x is prime. and Contra positive: If x is not odd then x is not a prime number.} \\ \text{Converse: If x is not odd then x is prime. and Contra positive: If x is not odd then x is not a prime number.} \\\text{ Converse: If x is odd then x is prime. and Contra positive: If x is not odd then x is a prime number.} \\ \text{Contra positive: If x is odd then x is prime. and Converse: If x is not odd then x is not a prime number.} \end{array} $

Answer 1

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 : If $x$ is prime then $x$ is odd.

Here $p\rightarrow$ $x$ is prime.

$q\rightarrow$ $x$ is odd.

$\Rightarrow\:$ ~$p\rightarrow\:$ $x$ is not prime and

~$q\rightarrow\:$ $x$ is not odd.

$\therefore$ The converse of this statement is:

If $x$ is odd then $x$ is prime. and

The contra positive of this statement is:

If $x$ is not odd then $x$ is not a prime number.