Question

Consider the statement: “For an integer$n$, if $n^3-1$ is even, then $n$ is odd.” 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$n$ is not even, then$n^3-1$ 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

Finding the contrapositive statement of the given statement.

$p:n^3-1$is even, $q:n$ is odd

Contrapositive of $p\to q=~q\to ~p$

⇒ If $n$ is not odd then $n^3-1$ is not even

⇒ For an integer $n$, if $n$ is even, then $n^3-1$ is odd

Hence, the correct option is$\left(D\right)$.