Biconditional connective truth table – UGC NET Question

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.