UGC NET Questions (Paper – 1)

The contrapositive of a conditional "if p, then q" is formed by negating both the antecedent and the consequent and reversing their positions, giving "if not q, then not p". In classical logic, a conditional and its contrapositive are always logically equivalent. This means they share the same truth table and stand or fall together. Hence the statement described is called the contrapositive.

Option A:
Option A, converse, yields "if q, then p" by swapping the antecedent and consequent without negating them. The converse is not necessarily equivalent to the original and thus does not match the pattern in the question.

Option B:
Option B, inverse, gives "if not p, then not q" by negating both parts but keeping their positions. Like the converse, the inverse is not generally equivalent to the original conditional. Therefore inverse is not the correct answer.

Option C:
Option C, biconditional, expresses "p if and only if q" and asserts both directions of implication in one statement. It is a different connective altogether and not merely a transformation of a single conditional.

Option D:
Option D is correct because contrapositive is the recognised name for the transformed conditional that is always logically equivalent to the original. This equivalence underlies many proof techniques.

The contrapositive of a conditional “if p, then q” is the statement “if not q, then not p”. In classical logic, a conditional and its contrapositive are always logically equivalent. This means they share the same truth table and stand or fall together. Therefore the transformed statement described in the stem is called the contrapositive.

Option A:
Option A correctly names contrapositive as the form obtained by negating and swapping antecedent and consequent. Because it preserves logical equivalence, it is widely used in proofs. Hence this option accurately answers the question.

Option B:
Option B, converse, is “if q, then p”, which only swaps the positions without negating them. The converse is not guaranteed to be equivalent to the original conditional. Thus converse is not the correct label here.

Option C:
Option C, inverse, is “if not p, then not q”, which negates both parts but does not interchange them. Like the converse, it is generally not equivalent to the original statement. Therefore inverse does not fit the description.

Option D:
Option D, biconditional, has the form “p if and only if q” and requires both directions of implication. It is a different connective, not just a transformation of a single conditional. Hence biconditional is not appropriate.