__3.3b Union of Sets__

**1.**The

**union**of set

*A*and set

*B*, denoted by

**A****υ**

*is the set consisting of*

**B**
all elements in set

*A*or set*B*or**both**the sets.
The Venn diagram of

*A*υ*B*is illustrated as below:**2.**The

**union**of set

*A*, set

*B*and set

*C*, denoted by

**A****υ**

*B*υ*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*υ*B*υ*C*is illustrated as below:**Example 1:**

The Venn diagram below shows the number of elements
in the universal set, ξ, set

*P*, set*Q*and*R*.
Given

*n*(*Q*) =*n*(*P*υ*R*)’, find*n*(ξ).

*Solution:**n*(

*Q*) =

*n*(

*P*υ

*R*)’

2

*x*+ 6 + 1 + 5 = 2*x*+ 2*x*
2

*x*+ 12 = 4*x*
2

*x*= 12*x*= 6

*n*(ξ) = 2

*x*+ 2

*x*+

*x*+ 7 + 6 + 1 + 5

= 5

*x*+ 19
= 5(6) + 19

= 30 + 19

=

**49****Example 2:**

Diagram below is a Venn diagram showing the
universal set, ξ = {Form 3 students}, set

*A*= {Students who play piano} and set*B*= {Students who play violin}.
Given

*n*(ξ) = 60,*n*(*A*) = 25,*n*(*B*) = 12 and*n*(*A*∩*B*) = 8, find the number of students who do not play the two instruments.

*Solution:*
The students who do not play the two instruments are
represented by the shaded region, (

*A*υ B)’.
Number of students who do not play the two
instruments

=

*n*(*A*υ*B*)’
= 60 – 17 – 8 – 4

=

**31**