__4.3a 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*.

**The**

2.

2.

**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*.

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

3.

3.

(a) P ∩ Q

$$

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

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

(d) P ∩ Q ∩ R

**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.