CHAPTER4: OPERATIONS ON SETS(4.2)

Chapter 4:
Operations on Sets

4.2 Union of sets

4.2.1 DETERMINE &
DESCRIBE THE UNION OF

SETS

Determine and describe the union of sets using various
representations

● The union of sets A and B is written using the symbol ⋃ .
● The union of set A and set B, denoted by A ⋃ B is the set consisting of all

elements in set A or set B or both the sets.
● The Venn diagram of A ⋃ B is illustrated as below:

A⋃B

Determine and describe the union of sets using various
representations

● The union of set A, set B and set C, denoted by A ⋃ B ⋃ C is the set consisting
of all elements in set A, set B or set C or all the three sets.

● The Venn diagram of A ⋃ B ⋃ C is illustrated as below:

A⋃B⋃C

More union of sets :

The union of two or more sets can be represented by the shaded regions in the
Venn diagrams below.

Example :

Example :

It is given that set P = {factors of 24}, set Q = {multiples of 3 which are less than 20} and
set R = {multiples of 4 which are less than 20}.

Draw a Venn diagram to represent sets P, Q and R, and shade the regions that represent the following

unions of sets. (ii) P ⋃ Q ⋃ R

(i) P ⋃ Q

Solution:

4.2.2 The Complement of the
Union of Sets

Describe the complement of the union of sets

● The complement of the union of sets is written as (A ⋃ B)', and is read as

“the complement of the union of sets A and B”.
● The complement of the union of sets A and B refers to all the elements NOT

in set A and set B.
● More Complement of the union of sets in Venn diagram as below:

Example :

Example :

Example :

Example :

SOLVING
PROBLEMS
INVOLVING THE
UNION OF SETS

More Example :

Solution:
n(Q) = n (P υ R)’
2x + 6 + 1 + 5 = 2x + 2x

2x + 12 = 4x
2x = 12
x=6

n(ξ) = 2x + 2x + x + 7 + 6 + 1 + 5
= 5x+ 19
= 5(6) + 19
= 30 + 19
= 49

More Example : **Draw a venn diagram to represent the problem
will be easier to understand the problem
A total of 26 pupils participate in a
scouting programme at the river U
bank. The activities of the
programme are kayaking and fishing. K 18-9
18 pupils participate in kayaking and
15 pupils participate in fishing while 9 F
pupils participate in both kayaking
and fishing. What is the total number 9
of pupils who participate in the
activities of the programme? x 15-9

Solution: Only kayaking = 18 - 9 = 9
Only fishing = 15 - 9 = 6
Total = 26 pupils
Kayaking = 18 x = Pupils do not involve any activities
Fishing = 15
Kayaking and fishing = 9 = 26 - 9 - 9 - 6
Calculate the total number pupils who participate =2
in activities of the programme. Therefore,
Total number of pupils participate in activities
= 26 - 2
= 24

OR

9+9+6
= 24

CONCLUSION:
n(K u F) = 24

To be continued :

4.3 Combined Operations on Sets