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.

Statements A and B are standard properties: a set includes itself as a subset and ∅ is a subset of every set. C is correct since a proper subset of a finite set must omit at least one element, so its cardinality is smaller. E is also correct because mutual inclusion implies equality of sets. D is false; no set is a proper subset of itself by definition. Thus A, B, C and E only are correct.

Option A:
Option A is incomplete because it omits E and therefore fails to mention the important characterisation of equality in terms of mutual subset relations, a common exam point.

Option B:
Option B is wrong since it adds D, which incorrectly states that a set can be a proper subset of itself, contradicting the strictness in the definition of “proper”.

Option C:
Option C is incorrect because it includes D and drops C, losing the crucial cardinality property of proper subsets and introducing the false claim that a set is a proper subset of itself.

Option D:
Option D is correct as it collects all true subset properties listed and excludes D, which conflicts with the standard definition of proper subset in set theory.

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.