Proof by contradiction method – UGC NET Question

Proof by contradiction is an indirect method of proof where we assume that the statement to be proved is false and then logically deduce a contradiction. This contradiction shows that the assumption of falsity cannot hold, so the original statement must be true. It is often used in proving results that are difficult to handle directly. Hence, the method described in the question is called proof by contradiction.

Option A:
Proof by induction is a different technique that involves a base step and an inductive step to show that a statement holds for all natural numbers. It does not rely on assuming the negation of the statement and reaching a contradiction. Therefore, induction does not match the description in the question.

Option B:
Proof by contradiction is correct because it fits exactly the process of assuming the negation and deriving an impossibility or inconsistency. For example, classic proofs of the irrationality of √2 use this method. Understanding this technique helps students tackle theoretical questions in mathematical reasoning.

Option C:
Proof by construction involves explicitly constructing an example or object that satisfies the required properties. It does not necessarily involve any assumption that the statement is false. Therefore, construction is conceptually different from the method described in the stem.

Option D:
Proof by example is typically used to demonstrate the existence of at least one object with a given property, but it cannot prove statements that are meant to hold universally. It also does not depend on assuming the negation and producing a contradiction. Thus, this option is not correct for the method mentioned.