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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). - CBSE (Arts) Class 11 - Mathematics

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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 n2 > 9 (by contradiction method).

Solution

The given statement, q, is as follows.

If n is a real number with n > 3, then n2 > 9.

Let us assume that n is a real number with n > 3, but n2 > 9 is not true.

That is, n2 < 9

Then, n > 3 and n is a real number.

Squaring both the sides, we obtain

n2 > (3)2

⇒ n2 > 9, which is a contradiction, since we have assumed that n2 < 9.

Thus, the given statement is true. That is, if n is a real number with n > 3, then n2 > 9.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 14: Mathematical Reasoning
Q: 6.2 | Page no. 345

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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.
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