Consider the statement: "For an integer n,

Question:

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

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

  2. (2) For an intetger $\mathrm{n}$, if $\mathrm{n}^{3}-1$ is not even, then $\mathrm{n}$ is not odd.

  3. (3) For an integer $\mathrm{n}$, if $\mathrm{n}$ is even, then $\mathrm{n}^{3}-1$ is even.

  4. (4) For an integer $\mathrm{n}$, if $\mathrm{n}$ is odd, then $\mathrm{n}^{3}-1$ is even.

Correct Option: 1

Solution:

(a) Contrapositive statement will be

"For an integer $n$, 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".

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