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Free Practice Set for Sets . This practice set contains questions that will cover most important topic of JEE Mains /Advance of this chapter. Syllabus : Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations. SETS : In mathematics, a set is a collection of elements. The most common methods used to describe sets are: The verbal description method. The roster notation or listing method. The set-builder notation. There are various kinds of sets like – finite and infinite sets, equal and equivalent sets, a null set. Further, there are a subset and proper subset, power set, universal set in addition to the disjoint sets. The power set of a set S is the set of all subsets of a set S, commonly written as P(S). S={1, 2, 3} has three elements, and its power set P(S) has 8 elements given by P(S)={∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}. Some basic properties of unions: (1)A ∪ B = B ∪ A. (2) A ∪ (B ∪ C) = (A ∪ B) ∪ C. (3) A ⊆ (A ∪ B) (4) A ∪ A = A. (5) A ∪ ∅ = A. (6) A ⊆ B if and only if A ∪ B = B. Some basic properties of intersections:(1) A ∩ B = B ∩ A. (2)A ∩ (B ∩ C) = (A ∩ B) ∩ C. (3)A ∩ B ⊆ A. (4)A ∩ A = A. (5)A ∩ ∅ = ∅. (6)A ⊆ B if and only if A ∩ B = A. If A and B are any two sets then, (1) (A ∪ B)′ = A′ ∩ B′ , the complement of A union B equals the complement of A intersected with the complement of B. (2) (A ∩ B)′ = A′ ∪ B′ , the complement of A intersected with B is equal to the complement of A union to the complement of B. The inclusion–exclusion principle is a counting technique that can be used to count the number of elements in a union of two sets—if the size of each set and the size of their intersection are known.