Set operations and cardinality – UGC NET Question

Statements A and B are the standard counting rules for unions of finite sets, with B capturing the special case of disjoint sets. Statement D is also correct because the elements of A and A' partition the universal set, so their cardinalities add up to its size. Statement C is false; A − B means elements in A but not in B, not the other way round. Statement E is false because if A is a subset of B, then A ∩ B' can be empty. Thus only A, B and D are correct, matching option D.

Option A:
Option A is incomplete since it omits D, which connects complements to the universal set and is an important counting identity in many exam questions. Without D the set of correct statements is not complete.

Option B:
Option B is incorrect because it includes C, which reverses the direction in the definition of set difference, thereby introducing a wrong statement into the combination.

Option C:
Option C is also wrong as it adds C and D to A and B, so it contains the incorrect interpretation of A − B along with true facts, and that makes the option invalid for “select the correct statements”.

Option D:
Option D is correct because it retains only the three accurate statements about union cardinalities and complements while excluding C and E, both of which misinterpret set difference or subset relations.