#### Question

Check the validity of the statements given below by the method given against it.

*q*: If *n* is a real number with *n* > 3, then *n*^{2} > 9 (by contradiction method).

#### Solution

The given statement, *q*, is as follows.

If *n* is a real number with *n* > 3, then *n*^{2} > 9.

Let us assume that *n* is a real number with *n* > 3, but *n*^{2} > 9 is not true.

That is, *n*^{2} < 9

Then, *n* > 3 and *n* is a real number.

Squaring both the sides, we obtain

*n*^{2} > (3)^{2}

⇒ *n*^{2} > 9, which is a contradiction, since we have assumed that *n*^{2} < 9.

Thus, the given statement is true. That is, if *n* is a real number with *n* > 3, then *n*^{2} > 9.

Is there an error in this question or solution?

Solution Check the Validity of the Statements Given Below by the Method Given Against It. Q: If N Is a Real Number With N > 3, Then N2 > 9 (By Contradiction Method). Concept: Validation by Contradiction.