Necessary and sufficient conditions – UGC NET Question

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.