Write the contrapositive and converse of the following statement:
If $x$ is a prime number,then $x$ is odd.
If $x$ is a prime number,then $x$ is odd.
(N/A) The given statement is of the form $P \implies Q$,where $P$ is '$x$ is a prime number' and $Q$ is '$x$ is odd'.
The contrapositive of $P \implies Q$ is $\neg Q \implies \neg P$.
Thus,the contrapositive is: If $x$ is not odd,then $x$ is not a prime number.
The converse of $P \implies Q$ is $Q \implies P$.
Thus,the converse is: If $x$ is odd,then $x$ is a prime number.
The contrapositive of $P \implies Q$ is $\neg Q \implies \neg P$.
Thus,the contrapositive is: If $x$ is not odd,then $x$ is not a prime number.
The converse of $P \implies Q$ is $Q \implies P$.
Thus,the converse is: If $x$ is odd,then $x$ is a prime number.
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