UGC NET Questions (Paper – 1)

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).

Statements A, C and D correctly explain basic Venn diagram ideas. A is true because Venn diagrams use overlapping closed curves to depict set relationships. C is correct as union collects elements from either set or both. D is also correct since the intersection consists of elements common to both sets. B is false because the common region represents intersection, not union, and E is false as the complement contains elements not in A. Thus A, C and D only are correct.

Option A:
Option A is incomplete since it omits D, leaving out the explicit description of intersection, which is fundamental to reading Venn diagrams. It therefore does not capture all the correct statements.

Option B:
Option B is incorrect because it includes only C and D and omits A, failing to mention what a Venn diagram is, and it also leaves out one of the true descriptive statements.

Option C:
Option C is correct as it gathers all the accurate statements about the depiction of sets, their union and intersection, while excluding B and E, which misidentify the regions and the meaning of complements.

Option D:
Option D is wrong because it includes E, which reverses the meaning of complement by saying it contains all elements of A, and therefore mixes a false statement with true ones.