Statement and Conclusion Equation – UGC NET Question

The contrapositive of a statement of the form “If p then q” is “If not q then not p,” and these two are logically equivalent. Here, p is “the number is divisible by 6” and q is “the number is divisible by 3.” The contrapositive is therefore “if a number is not divisible by 3, then it is not divisible by 6.” This preserves the logical structure of the original implication while reversing and negating its components.

Option A:
Option A negates p but not q and forms the inverse “If not p then not q,” which is not logically equivalent to the original statement in general.

Option B:
Option B correctly follows the contrapositive pattern ¬q → ¬p, matching the structure of the initial implication about divisibility. It reflects the fact that if a number is not divisible by 3, it cannot possibly be divisible by 6.

Option C:
Option C is the converse q → p, which need not be true simply because the original implication is true; many numbers are divisible by 3 but not by 6.

Option D:
Option D contradicts the original statement directly by combining p with not q, which cannot be true if the original implication holds.