UGC NET Questions (Paper – 1)

Statements A, B, C and D accurately describe reductio ad absurdum and its relation to prasaṅga, while E is false. In reductio, we assume the opposite of what we want to prove and derive a contradiction or absurd consequence, forcing us to reject that assumption and accept its negation. Buddhist prasaṅga uses a similar technique against an opponent’s thesis. However, merely having contradictory premises does not automatically constitute a proper reductio; the contradiction must be shown to arise from the specific assumption under test. Thus E is the only incorrect statement.

Option A:
Option A is correct because it singles out E as the sole wrong statement and preserves the correct description of reductio and its dialectical use in A, B, C and D. This option mirrors the structured method taught for proof by contradiction.

Option B:
Option B is incorrect since it also marks C as wrong even though C correctly states what is concluded when a contradiction arises from the assumed negation. C and E only therefore misclassifies a crucial step in reductio as incorrect.

Option C:
Option C is wrong because it treats D as wrong along with E, despite D accurately noting the use of prasaṅga in Buddhist debates. D and E only thus fails to respect the historical connection.

Option D:
Option D is also incorrect since it includes B among the wrong statements, even though B correctly explains that we derive a contradiction or unacceptable consequence from the assumption. B, D and E only therefore cannot be accepted as the correct answer.

A correctly describes contradiction: assume the negation of what you want to prove and reach a contradiction. B is correct: proving the contrapositive is equivalent to proving the original conditional. D is correct: both are valid classical methods. C is false because contradiction proves the conclusion true (not both premises and conclusion false). E is false because contradiction proofs can be valid even when non-constructive. Therefore A, B and D only are correct.

Option A:
Option A is incomplete because it omits D, the statement confirming both methods are valid.

Option B:
Option B is incorrect because it includes C, which misstates the outcome of a contradiction proof.

Option C:
Option C is wrong because it omits A, leaving out the defining idea of contradiction.

Option D:
Option D is correct because it includes exactly the true statements and excludes C and E, which are false.

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.