Necessary and sufficient conditions – UGC NET Question

Statements A, B and C present the standard relationships between necessary and sufficient conditions. A is correct because sufficiency ensures Q whenever P holds. B is true since necessity means Q cannot hold without P. C is correct as “necessary and sufficient” expresses logical equivalence. D is false; sufficiency does not generally reverse, and E is false because in “if P then Q”, P is sufficient and Q is necessary. Thus, A, B and C only are correct.

Option A:
Option A is incomplete because it omits C, and therefore does not explicitly mention the important notion of equivalence when a condition is both necessary and sufficient.

Option B:
Option B is incorrect because it includes E, which reverses the roles of P and Q in the implication, so this option accepts a false description of necessary and sufficient conditions.

Option C:
Option C is correct as it collects all three accurate conceptual definitions and excludes D and E, which misrepresent the direction and roles in implications.

Option D:
Option D is wrong since it adds D, which claims sufficiency reverses, and so includes a clear logical error alongside true statements, making the combination unacceptable.