We know that arithmetics has operations of addition, subtraction, multiplication and division
of numbers. Similarly in sets, we define the operation of union, intersection and difference of sets.
2.6.1 UNION OF SETS
Let us consider m , the set of all students in your school.
Suppose A is the set of students in your class who were absent on Tuesday and B is the
set of students who were absent on Wednesday. Then,
Let A = {Roja, Ramu, Ravi} and
Let B = {Ramu, Preethi, Haneef}
Now, we want to find K, the set of students who were absent on either Tuesday or
Wednesday. Then, does Roja ∈ K? Ramu ∈ K? Ravi ∈ K? Haneef ∈ K? Preethi ∈ K?
Akhila ∈ K?
Roja, Ramu, Ravi, Haneef and Preethi all belong to
K but Akhila does not.
Hence, K = {Roja, Ramu, Ravi, Haneef , Preethi}
Here, the set K is the called the union of sets A and
B. The union of A and B is the set which consists of all the
elements of A and B. The symbol ‘È’ is used to denote the union. Symbolically, we write A È B
and usually read as ‘A union B’ or A cup B.
A ∪ B = {x : x ∈ A or x &isinB}
Example-1.
Let A = {2, 5, 6, 8} and B = {5, 7, 9, 1}. Find A ∪ B.
Solution :
We have A ∪ B = {2, 5, 6, 8} È {5, 7, 9, 1}
= {2, 5, 6, 8, 5, 7, 9, 1}
= {1, 2, 5, 6, 7, 8, 9}.
Note that the common element 5 was taken only once while writing A ∪ B.
Example-2.
Let A = {a, e, i, o, u} and B = {a, i, u}. Show that A ∪ B = A.