UGC NET Questions (Paper – 1)

Statements A and B state the two standard De Morgan identities for sets. Statement C is correct because these laws explicitly relate complements of unions and intersections. Statement E is also true; in Venn diagrams one can see that the shaded regions for both sides of each law coincide. Statement D is false since De Morgan’s laws hold in general, not only for finite sets. Hence the correct set of statements is A, B, C and E only, corresponding to option A.

Option A:
Option A is correct because it collects the two algebraic forms of the laws, their conceptual role and their Venn-diagram visualisation, while rightly excluding D, which wrongly restricts them to finite sets.

Option B:
Option B is incomplete as it omits E and so fails to mention the important geometric interpretation in Venn diagrams, which is often tested in NET questions on sets.

Option C:
Option C is incorrect because it includes D, the false claim about failure for infinite sets, and so mixes correct principles with an incorrect limitation.

Option D:
Option D is wrong since it leaves out A and picks only B, C and E; without A, one of the two core algebraic identities of De Morgan’s laws is missing, so the description is not complete.

Statements A and B are the precise symbolic forms of De Morgan’s laws for sets. E is also correct because it broadly describes the role of De Morgan’s laws in relating complements to unions and intersections. C and D are false since they swap union/intersection incorrectly: the complement of a union is an intersection of complements, and the complement of an intersection is a union of complements. Hence A, B and E only are correct.

Option A:
Option A is incomplete because it leaves out E and therefore omits the general conceptual summary of what De Morgan’s laws do.

Option B:
Option B is wrong because it adds C, which contradicts De Morgan’s law for complements of unions.

Option C:
Option C is correct as it selects exactly those statements that align with De Morgan’s laws and excludes C and D, which misuse union and intersection in the context of complements.

Option D:
Option D is incorrect since it omits A (a true De Morgan law), so it cannot be correct.

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.