Class 10 Maths · Proofs in Mathematics · NCERT Exercise A1.6 · Question 3

Proofs in Mathematics Medium

Use proof by contradiction to prove that if for an integer

a

a^{2}

is even, then so is

a

. [Hint: Assume

a

is not even, that is, it is of the form

2 n + 1

, for some integer

n

, and then proceed.]

Answer

Proved by contradiction: assuming

a = 2 n + 1

gives

a^{2} = 2 (2 n^{2} + 2 n) + 1

, which is odd and contradicts

a^{2}

being even, so

a

must be even.

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