UGC NET Questions (Paper – 1)

The phrase “p if and only if q” asserts both “if p, then q” and “if q, then p”. In propositional logic, this two-way connection is expressed by the biconditional connective. A biconditional is true exactly when both components share the same truth value. Therefore the compound statement in the stem is called a biconditional.

Option A:
Option A, disjunction, joins statements with “or” and does not require them to share truth values. It lacks the two-way commitment of “if and only if”. Thus disjunction is not the correct answer.

Option B:
Option B, implication, represents the one-way conditional “if p, then q”. It does not capture the reverse implication from q to p. Hence implication alone does not fit the form described.

Option C:
Option C correctly names biconditional as the connective corresponding to “if and only if”. It combines two conditionals into a single equivalence statement. Therefore biconditional is the best choice here.

Option D:
Option D, negation, simply reverses the truth value of a single statement. It cannot express a mutual dependence between two propositions. Consequently negation is not suitable.

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.

A biconditional statement links two propositions in such a way that each implies the other. The form "p if and only if q" means that p is true exactly when q is true and false exactly when q is false. This captures a strong equivalence relation between the two. Therefore the compound statement described in the stem is called a biconditional.

Option A:
Option A, disjunctive, refers to a statement formed with "or", which is true when at least one of its disjuncts is true. It does not require mutual implication or matching truth values in the way a biconditional does. Hence disjunctive is not the correct answer.

Option B:
Option B, conjunctive, denotes a statement formed with "and" where both components must be true, but it does not capture the idea that each condition guarantees the other’s truth. Conjunction lacks the mutual equivalence of "if and only if".

Option C:
Option C, conditional, refers to one-way implication of the form "if p, then q". While a biconditional includes two such conditionals, the term conditional alone does not express the bi-directional nature specified in the question.

Option D:
Option D is correct because biconditional precisely names the connective that asserts "p if and only if q". Its truth table reflects equality of truth values between the component propositions and embodies logical equivalence.

A, B, C and E are correct. D is false because natural language uses of “if/only if” can be looser than strict logical operators. Therefore the correct combination is A, B, C and E only.

Option A:
Option A is incomplete because it omits E (exam translation importance).

Option B:
Option B is incorrect because it includes D (false).

Option C:
Option C is correct because it includes all true statements and excludes D.

Option D:
Option D is incorrect because it omits A, so it is incomplete.