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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.
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