Biconditional statements properties – UGC NET Question

Statements A, B and D all accurately describe biconditional statements. A gives the overall truth condition: both sides must match in truth value. B shows that “if and only if” can be written as the conjunction of two implications. D restates the falsity condition: the biconditional fails when P and Q differ in truth. C is false because “P or Q” is true in more cases than “P if and only if Q”, and E is false because biconditionals are not tautologies. Hence A, B and D only are correct.

Option A:
Option A is incomplete because it omits D, so it fails to mention explicitly when the biconditional is false, which is essential for constructing its truth table.

Option B:
Option B is incorrect as it includes only B and D and omits A, losing the succinct characterisation that biconditional is true exactly when P and Q agree.

Option C:
Option C is wrong because it adds E, which incorrectly asserts that biconditionals are always true, and it therefore includes at least one false statement.

Option D:
Option D is correct as it brings together the equivalence in terms of matching truth values, the conjunction of implications and the falsity condition, while excluding C and E, which misrepresent the biconditional.