Proof by contrapositive strategy – UGC NET Question

Proof by contrapositive exploits the logical equivalence between a conditional and its contrapositive. Instead of proving "if p, then q" directly, one proves "if not q, then not p". Because these two statements share the same truth conditions, demonstrating the contrapositive suffices to establish the original conditional. Thus the method described is called proof by contrapositive.

Option A:
Option A, proof by cases, involves dividing a problem into exhaustive possibilities and proving the desired conclusion in each case. While also a valid strategy, it does not focus on transforming a conditional into its contrapositive. Hence cases is not correct.

Option B:
Option B, proof by contradiction, proceeds by assuming the negation of what is to be proved and deriving a contradiction, thereby showing the assumption must be false. This is a distinct method and does not necessarily proceed via contrapositive structure.

Option C:
Option C is correct because proof by contrapositive explicitly names the strategy of proving the contrapositive to justify the original "if p, then q". It leverages the equivalence relation discussed earlier and is particularly useful when the direct approach is difficult.

Option D:
Option D, proof by example, at most shows that a statement is true in one or some instances and is usually insufficient to establish universal claims. It does not relate to the contrapositive transformation.