UGC NET Questions (Paper – 1)

Statements A, B, C and E correctly characterise the biconditional connective. A and C together state that p ↔ q is true when p and q match in truth value and false otherwise. B is correct since p ↔ q decomposes into (p → q) and (q → p). E is true because swapping p and q in a biconditional does not change its meaning. D is false; with two propositional variables, the truth table has four rows, and the biconditional is true in exactly two of them (both true or both false), not three. Therefore, A, B, C and E only form the correct set.

Option A:
Option A is correct because it collects all four accurate properties and excludes D, which miscounts the true rows of the biconditional. It matches the logical behaviour of “if and only if” as tested in NET reasoning.

Option B:
Option B is incomplete as it leaves out E, so it does not mention the commutative nature of the connective, even though that is an important structural property. Without E, the description is not fully comprehensive.

Option C:
Option C is incorrect because, while B and C and E are true, it omits A, which directly states the key condition about matching truth values. The option therefore does not explicitly identify the central truth condition of the biconditional.

Option D:
Option D is wrong because it retains D, the statement that there are three true rows, which is factually incorrect, and it omits B. Once a wrong statement is included, the option cannot represent the exact set of correct statements.

Statements A, B, C and E correctly state the truth conditions and logical role of biconditionals, while D is false. “If and only if” requires that p and q share the same truth value, which can be expressed as two conditionals taken together. It is false exactly when one is true and the other false. Far from being only sufficient, p is both necessary and sufficient for q in a biconditional, so D misdescribes the relation. Recognising this helps with equivalence transformations in UGC NET questions.

Option A:
Option A is incomplete because it omits E, not mentioning how biconditionals feature in exam-style equivalence problems. A, B, C only therefore leaves out a key application of the concept.

Option B:
Option B is wrong since it drops A, thereby failing to state in general that biconditionals are true when p and q match in truth value. B, C, E only provides specific and exam-related facts but lacks the core truth-condition statement.

Option C:
Option C is correct as it gathers all the true statements and excludes D, which restricts the relation to sufficiency alone. This option aligns with standard propositional logic and how biconditionals are tested in symbolic reasoning questions.

Option D:
Option D is incorrect because it omits B, losing the important equivalence of a biconditional with two conditionals. A, C, E only is therefore not acceptable as the right answer.