(B) The contrapositive of a conditional statement $(p \rightarrow q)$ is defined as $(\sim q \rightarrow \sim p)$.Here,$p$ is the statement "$n^{3}-1$

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For an integer $n$,if $n$ is even,then $n^{3}-1$ is odd.

(B) The contrapositive of a conditional statement $(p \rightarrow q)$ is defined as $(\sim q \rightarrow \sim p)$.Here,$p$ is the statement "$n^{3}-1$ is even" and $q$ is the statement "$n$ is odd".The negation $\sim q$ is "$n$ is not odd",which means "$n$ is even".The negation $\sim p$ is "$n^{3}-1$ is not even",which means "$n^{3}-1$ is odd".Therefore,the contrapositive statement is: "For an integer $n$,if $n$ is even,then $n^{3}-1$ is odd."

Class 11 Mathematics Mathematical Reasoning Mathematical logic

Medium

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

JEE MAIN 2020 All JEE MAIN

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

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

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