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 give correct definitions of union and intersection, D correctly states that the empty set is a subset of every set and E is true because many reasoning problems about groups naturally use set models and sometimes Venn diagrams. Statement C is false since the complement of A in U consists of elements of U that are not in A, not elements that are in both A and U. Therefore, the combination A, B, D and E only is correct.

Option A:
Option A is incomplete because it omits E and so does not mention the common application of set theory to practical reasoning questions in exams. Without E, the conceptual link to aptitude problems is weakened.

Option B:
Option B is also incomplete as it leaves out A and therefore fails to give the basic description of union, which is central to understanding combined categories in reasoning questions.

Option C:
Option C is wrong because it includes C, which misdescribes complement, and omits E, ignoring the modelling role of sets. Including a false statement invalidates the option.

Option D:
Option D is correct as it keeps all true statements while excluding C, the incorrect account of complement. It aligns with the formal set-theoretic framework used for UGC NET reasoning items.