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, B and C are standard interpretations of sets, universal set and complement using Venn diagrams. Statement E is also true because Venn diagrams are widely used to visualise logical relations and survey data. Statement D is false since disjoint sets have no shared elements and thus no overlapping regions in the diagram. Hence the combination A, B, C and E only is correct.

Option A:
Option A is correct as it combines all accurate statements while rejecting D, which misdescribes disjointness. It faithfully reflects how Venn diagrams are used in NET-style reasoning questions.

Option B:
Option B is incomplete because it omits E and therefore does not mention important applications such as classification and survey questions, limiting the scope of the description.

Option C:
Option C is wrong because it includes D, which contradicts the definition of disjoint sets by asserting that they overlap, even though it also lists true statements. The presence of D invalidates the option.

Option D:
Option D is also incorrect as it keeps D and omits A, thereby losing the basic fact about sets as regions and retaining an incorrect claim about disjointness.

A is correct because subset means every element of A belongs to B. D is true as the empty set, having no elements, vacuously satisfies the subset condition for any set. E is also correct because mutual inclusion implies equality of sets. B is false since a proper subset is strictly smaller than the set, and C is false because the universal set contains all elements, so other sets are subsets of U, not the other way round. Thus A, D and E only are correct.

Option A:
Option A lists A and D but omits E, failing to express how mutual subset relations guarantee equality. Without E, the account of subset relations is incomplete.

Option B:
Option B includes A and E but omits D, ignoring the important property of the empty set as a subset of every set. This makes the combination less comprehensive.

Option C:
Option C is correct because it combines all three true statements and excludes B and C, which misrepresent proper subset and universal set roles. It fully reflects the basic set relations used in reasoning questions.

Option D:
Option D includes only D and E, omitting A, and therefore does not explicitly state what it means for A to be a subset of B. This leaves out a fundamental definition.

Statements A and B give the two De Morgan identities for complements of unions and intersections. Statement C correctly notes that these laws link complements with union and intersection operations. Statement D is also true because the universal set’s complement is the empty set relative to that universe. Statement E is false since similar De Morgan laws hold for logical connectives “and” and “or”. Thus A, B, C and D only are correct.

Option A:
Option A is correct because it gathers all the true statements and excludes E, which wrongly denies the logical counterpart of De Morgan’s laws.

Option B:
Option B is incomplete as it omits D (complement of universal set).

Option C:
Option C is wrong because it includes E (false).

Option D:
Option D is wrong because it includes E (false) and omits A (one of the two key identities).