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-3.
If A = {1, 2, 3, 4} and B = {2, 4, 6, 8}. Find A ∪ B.
Solution : A = {1, 2, 3, 4} and B = {2, 4, 6, 8}
then A ∪ B = {1, 2, 3, 4}∪{2, 4, 6, 8}
= {1, 2, 3, 4, 2, 4, 6, 8}
= {1, 2, 3, 4, 6, 8}
2.6.2 INTERSECTION OF SETS
Let us again consider the example of students who were absent. Now let us find the set L
that represents the students who were absent on both Tuesday and Wednesday. We find that
L = {Ramu}.
Here, the set L is called the intersection of sets A and B.
In general, the intersection of sets A and B is the set of all
elements which are common in both A and B. i.e., those elements
which belong to A and also belong to B. We denote intersection
symbolically by as A ∩ B (read as “A intersection B”).
i.e., A ∩B = {x : x ∈ A and x ∈ B}
The intersection of A and B can be illustrated using the Venn-diagram as shown in the
shaded portion of the figure, given below, for Example 5.
Example-4.
Find A ∈ B when A = {5, 6, 7, 8} and B = {7, 8, 9, 10}.
Solution :
The common elements in both A and B are 7 and 8.
therefore A ∈ B = {5, 6, 7, 8} Ç {7, 8, 9, 10} = {7, 8}
(common elements)
Example-5. If A = {1, 2, 3} and B = {3, 4, 5}, then illustrate
A Ç B in Venn-diagrams.
Solution :The intersection of A and B can be illustrated in the
Venn-diagram as shown in the adjacent figure.
DISJOINT SETS
Suppose A = {1, 3, 5, 7} and B = {2, 4, 6, 8}. We see
that there are no common elements in A and B. Such sets are
known as disjoint sets. The disjoint sets can be represented by
means of the Venn-diagram as follows: