be the set of students of Class XI, who are in school hockey team. Let Y = {Geeta, David, Ashok} be the set of students from Class XI who are in the school football team. Find X ∪ Y and interpret the set. Solution We have, X ∪ Y = {Ram, Geeta, Akbar, David, Ashok}.
This is the set of students from Class XI who are in the hockey team or the football team or both. SETS Thus, we can define the union of two sets as follows: Definition The union of two sets A and B is the set C which consists of all those elements which are either in A or in B (including those which are in both). In symbols, we write. A ∪ B = { x : x ∈ A or x ∈ B } The union of two sets can be represented by a Venn diagram as shown in Fig .
. The shaded portion in Fig . represents A ∪ B. Some Properties of the Operation of Union A ∪ B = B ∪ A (Commutative law) ( A ∪ B ) ∪ C = A ∪ ( B ∪ C) (Associative law ) (iii) A ∪ φ = A (Law of identity element, φ is the identity of ∪ ) (iv) A ∪ A = A (Idempotent law) (v) U ∪ A = U (Law of U) .
. Intersection of sets The intersection of sets A and B is the set of all elements which are common to both A and B. The symbol ‘ ∩ ’ is used to denote the intersection . The intersection of two sets A and B is the set of all those elements which belong to both A and B.
Symbolically, we write A ∩ B = { x : x ∈ A and x ∈ B}. Example Consider the sets A and B of Example . Find A ∩ B. Solution We see that , are the only elements which are common to both A and B.