are subsets, and also B ⊂ A. The reader will see an extensive use of the Venn diagrams when we discuss the union, intersection and difference of sets. . Operations on Sets In earlier classes, we have learnt how to perform the operations of addition, subtraction, multiplication and division on numbers.
Each one of these operations was performed on a pair of numbers to get another number. For example, when we perform the operation of addition on the pair of numbers and , we get the number . Again, performing the operation of multiplication on the pair of numbers and , we get . Similarly, there are some operations which when performed on two sets give rise to another set.
We will now define certain operations on sets and examine their properties. Henceforth, we will refer all our sets as subsets of some universal set. . .
Union of sets Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once. The symbol ‘ ∪ ’ is used to denote the union . Symbolically, we write A ∪ B and usually read as ‘ A union B ’ .
Example Let A = { , , , } and B = { , , , }. Find A ∪ B. Solution We have A ∪ B = { , , , , , } Note that the common elements and have been taken only once while writing A ∪ B. Example Let A = { a, e, i, o, u } and B = { a, i, u }.
Show that A ∪ B = A Solution We have, A ∪ B = { a, e, i, o, u } = A. This example illustrates that union of sets A and its subset B is the set A itself, i.e., if B ⊂ A, then A ∪ B = A. Example Let X = {Ram, Geeta, Akbar}