Question

Consider the statement $:$ ${}^{\prime \prime }$For an integer $n$, if $n^3-1$ is even, then $n$ is odd${}^{\prime \prime }$. The contrapositive statement of this statement is :

• A. For an integer $n$, if $n$ is even, then $n^3-1$ is even
• B. For an integer $n$, if $n$ is odd, then $n^3-1$ is even
• C. For an integer $n$, if $n^3-1$ is not even, then $n$ is not odd.
• D. For an integer $n$, if $n$ is even, then $n^3-1$ is odd

Answer 1

The correct option is D For an integer $n$, if $n$ is even, then $n^3-1$ is odd

$p:n^3-1$ is even, $q:n$ is odd
Contrapositive of $p\to q$ is $\sim q\to \sim p$
$\Rightarrow$ Contrapositive of the given statement is :
If $n$ is not odd, then $n^3-1$ is not even.
or, For an integer $n$, if $n$ is even, then $n^3-1$ is odd.