__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.

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

$\text{(b)}Q\subset P,\text{then}P\cap Q=Q$

$\begin{array}{l}\text{(c)}P\cap Q=\varnothing \text{,}\\ \text{Thereisnointersectionbetweenset}P\text{andset}Q\text{.}\end{array}$

**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)**