To prove that 'If \(n^2\) is even, then n is even', a teacher begins by assuming that \(n^2\) is even but 'n' is odd and then proceeds to show how this assumption is not possible. It is an example of proof by :
Contradiction
Proof by contradiction begins by assuming the opposite of what is to be proved and then shows that this assumption leads to a logical inconsistency.
Here, the teacher wants to prove that if n squared is even, then n is even, so the assumption made is that n squared is even while n is odd.
The teacher then shows that this assumption cannot hold, since an odd number squared is always odd, which contradicts the assumption that n squared is even.
Because the proof proceeds by assuming the opposite of the conclusion and disproving it, this is a proof by contradiction, and not induction, deduction, or verification.
Hence, the example given is of proof by contradiction.
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