Implications contrapositive and equivalence – UGC NET Question

Statement A pairs a conditional with its contrapositive, so they are logically equivalent. D is correct because logical equivalence by definition means matching truth values across all valuations. E is also true since a conditional and its contrapositive have identical truth conditions, so if the contrapositive is false, the original conditional must be false. B is wrong because its converse is not always true (an even number need not be divisible by 4), and C is wrong because a conditional is not generally equivalent to its converse. Thus A, D and E only form the correct combination.

Option A:
Option A is correct as it lists precisely the statements that capture equivalence with the contrapositive and the notion of equal truth values, while excluding B and C, which overstate the reliability of converses.

Option B:
Option B is incorrect because it adds B, which asserts that the converse of the divisibility statement is always true, even though simple counterexamples like 6 show this is false.

Option C:
Option C is wrong since it brings in C, which claims conditional and converse are always equivalent, contradicting standard logic, so the combination cannot be correct.

Option D:
Option D is incorrect as it omits A and includes B, thereby dropping a correct contrapositive-equivalence example and admitting a false statement about divisibility.