UGC NET Questions (Paper – 1)

A is the standard inclusion–exclusion formula for two sets. B is a special case when A and B are disjoint (intersection is empty). C is true because an intersection cannot have more elements than either set. D is true for subset relations. E is false because inclusion–exclusion is commonly extended to three (and more) sets. Therefore, A, B, C and D only are correct.

Option A:
Option A is incomplete because it omits D, which is also a true statement about subset relations with union and intersection.

Option B:
Option B is correct because it includes all true statements (A, B, C, D) and excludes E, which is false.

Option C:
Option C is incomplete because it omits A, which is a key identity for set cardinality.

Option D:
Option D is wrong because it includes E (false), so it cannot be the correct set.

Statement A gives the definition of the Cartesian product using ordered pairs with components from A and B. Statement B correctly states that the number of such pairs equals the product of the set sizes when the sets are finite. Statement C is also correct since a relation is any subset of A × B, with functions being special cases. Statement D is false because many relations are not functional, and E is false because A × B and B × A generally differ as ordered pairs reverse coordinates. Therefore, A, B and C only are correct, as in option B.

Option A:
Option A is incomplete because it omits C and so fails to connect the notion of relation with the Cartesian product, which is a key conceptual bridge in discrete mathematics.

Option B:
Option B is correct since it collects the definition of A × B, the counting rule for finite sets and the identification of relations as subsets, while excluding D and E, which confuse relations with functions and swap the order of products.

Option C:
Option C is incorrect because it includes D (false: not every relation is a function) and omits B (true: the counting rule), so it neither matches the correct set nor covers all correct statements.

Option D:
Option D is wrong because it includes E (false: A × B is not always equal to B × A) and omits A (the basic definition), so it mixes errors with omissions.