In the proof of (\sqrt{2}), which statement is a middle step rather than the final conclusion?

(a) is even

In the standard proof that \(\sqrt{2}\) is irrational, we first suppose that \(\sqrt{2}=a/b\), where \(a\) and \(b\) have no common factor. Squaring gives \(a^2=2b^2\), so \(a^2\) is even and therefore \(a\) is even. Writing \(a=2k\) then shows that \(b\) is also even. This is an intermediate step in the chain of reasoning, not the final statement.

Option B is correct because “\(a\) is even” is reached during the proof. The final contradiction is that both \(a\) and \(b\) are even, which conflicts with the assumption that \(a/b\) was in lowest terms. Consequently, the original rational assumption is false and \(\sqrt{2}\) is irrational. Options A and C express final conclusions, while D describes the contradiction itself.

This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Proof of irrationality of square root 2 and square root 3.