__3.3a Intersection of Sets__

**1.**The

**intersection**of set

*P*and set

*Q*, denoted by $P\cap Q$ is the set consisting of all elements common to set

*P*and set

*Q*.

**2.**The

**intersection**of set

*P*, set

*Q*and set

*R*, denoted by $P\cap Q\cap R$ is the set consisting of all elements common to set

*P*, set

*Q*and set

*R*.

**3.**Represent the intersection of sets using Venn diagrams.

$\text{(a)}P\cap Q$

$$

(b)
Q
⊂
P
,
then
P
∩
Q
=
Q

$\begin{array}{l}\end{array}$

(c)
P
∩
Q
=
∅
,
There is no intersection between set
P
and set
Q
.

**Example 1:**

Given that

*A*= {3, 4, 5, 6, 7},*B*= {4, 5, 7, 8, 9, 12} and*C*= {3, 5, 7, 8, 9, 10}.**(a)**Find

*A*∩

*B*∩

*C*.

**(b)**Draw a Venn diagram to represent

*A*∩

*B*∩

*C*.

*Solution:***(a)**

*A*∩

*B*∩

*C*= {5, 7}

**(b)**

**4.**The

**complement**of the intersection of two sets,

*P*and

*Q*, represented by

**(**, is a set that consists of all the elements of the universal set, ξ, but

*P*∩*Q*)’**not**the

**elements of**

*P*∩

**Q.****5.**The complement of set (

*P*∩

*Q*)’ is represented by the shaded region

as shown in the Venn diagram.