UGC NET Questions (Paper – 1)

Statements A, B and C correctly define sufficient and necessary conditions and note that a condition can sometimes be both. E is also true because many exam questions exploit this confusion. D is false, since “only if” generally indicates a necessary condition, not a sufficient one. Therefore the correct set of true statements is A, B, C and E only.

Option A:
Option A is correct because it includes all the accurate definitional statements and the exam-focused remark, while excluding D which reverses the usual reading of “only if”. It captures both conceptual clarity and test relevance.

Option B:
Option B is incomplete as it leaves out C, ignoring cases where a condition is both necessary and sufficient, so it does not gather all correct statements.

Option C:
Option C omits A, failing to state what a sufficient condition does, and therefore cannot be fully correct even though it retains some true statements.

Option D:
Option D excludes B, losing the definition of a necessary condition, so A, C and E only does not contain all true statements.

Statements A, B, C, D and E are all correct descriptions of necessary and sufficient conditions, whereas F is false. Sufficiency requires that p’s truth guarantees q, and necessity means q is required for p. When a condition is both necessary and sufficient, the two statements are equivalent, and such cases do exist in logic and mathematics. Misunderstanding these notions can easily produce fallacies in exam questions, so E is also correct, while F contradicts the definition of a necessary condition by suggesting an impossible relation.

Option A:
Option A is incomplete because it omits E, failing to include the practically important warning about exam inferences. While A, B, C and D correctly outline theoretical relations, they do not address how confusion between them leads to mistakes in reasoning. Therefore A, B, C and D only does not contain all the correct statements provided.

Option B:
Option B is correct since it gathers all five true statements A, B, C, D and E and excludes F, which misrepresents necessity. It integrates the conceptual link between necessity, sufficiency and equivalence with the practical impact on inferential errors. Thus it accurately reflects the understanding expected in UGC NET Paper 1.

Option C:
Option C is incorrect because it leaves out D, which notes that a condition may indeed be both necessary and sufficient in certain contexts. Without D, the answer ignores an important nuance about how conditions can combine. The omission means this option does not fully represent the set of correct statements.

Option D:
Option D is wrong because it omits A, the basic link between sufficiency and conditional implication, and includes only B, C, D and E. Without A, the account of sufficient conditions is incomplete, even though the other four statements are true. Hence B, C, D and E only cannot be the right combination.

Hetvābhāsa literally means “semblance of a reason.” It denotes a middle term that looks like a proper hetu but, on analysis, fails to meet the criteria for a valid inferential link. Such a reason might superficially satisfy some conditions or persuade the untrained, yet it does not secure the intended conclusion. Recognising hetvābhāsas is essential for diagnosing fallacies and maintaining rigour in debate.

Option A:
Option A describes a genuine hetu that meets trairūpya conditions; that is precisely what a hetvābhāsa is not.

Option B:
Option B correctly captures the deceptive nature of hetvābhāsa as a reason that has the appearance of validity but lacks true inferential force.

Option C:
Option C refers to dṛṣṭānta, the example offered to illustrate vyāpti; this is distinct from the middle term itself.

Option D:
Option D describes vyāpti, the invariable concomitance that underlies proper inference, whereas hetvābhāsa arises when this relation is missing or misapplied.

Statements A and C are correct because the contrapositive “If not q then not p” is logically equivalent to “If p then q”, and the inverse is indeed “If not p then not q”. Statement D is also true as many reasoning errors arise from confusing the converse “If q then p” with the contrapositive. Statement B is false because it mislabels the converse, and E is false because the contrapositive of a true implication is also true, not always false. Therefore, the combination A, C and D only is correct.

Option A:
Option A is correct since it gathers exactly the true statements about how converse, inverse and contrapositive are defined and how confusion among them can cause mistakes, while rejecting B and E, which misdescribe these relationships.

Option B:
Option B is incorrect as it includes B, which wrongly defines the converse, and thereby endorses a mislabelling of basic logical forms. Even though A and C are true, the presence of B ruins the option.

Option C:
Option C is wrong because it treats B, C and D as correct together, despite B being false. It also omits A, which explains the logical equivalence between an implication and its contrapositive, a central concept in NET-level logic.

Option D:
Option D is also incorrect because it includes E, which mistakenly claims that the contrapositive of a true implication is always false, and omits C, leaving out the correct statement of the inverse. This mixture makes the option unsound.