Only if and biconditional meanings – UGC NET Question

Statements A, B, C and D correctly relate “if”, “only if” and necessary conditions to their symbolic forms, and F is also true, while E is false. The biconditional is true exactly when p and q share the same truth value, not when they differ. Treating “only if” carefully is crucial for distinguishing what is necessary from what is sufficient. Hence the correct set of statements is A, B, C, D and F only.

Option A:
Option A is incomplete because it omits D and F, leaving out both the explicit link to necessary conditions and the exam relevance of misreading “only if”. Although A, B, C and E mention some relationships, they include E, which wrongly states the truth pattern of the biconditional. This makes the option incorrect.

Option B:
Option B is wrong because it includes E, which claims that “p if and only if q” is true when p and q differ in truth value. That is the truth condition for exclusive disjunction, not for the biconditional. Including E makes the combination logically inconsistent.

Option C:
Option C is correct as it gathers A, B, C and D, which correctly express equivalences and necessary condition symbolism, and F, which notes the importance of reading these connectives properly in exams. It excludes E, avoiding the confusion between biconditional and exclusive or. This matches standard logical teaching.

Option D:
Option D is incorrect since it omits A and replaces it with B, C, D, E and F. Without A, the equivalence of “p only if q” with “If p then q” is not stated, and including E still misrepresents the truth conditions of the biconditional. Therefore it cannot be the right answer.