This lesson will explain how to find the intersection of sets. We will start with a definition of the intersection of two sets

Given two sets A and B, the intersection is the set that contains elements or objects that belong to A and to B at the same time

We write A Ç B

Basically, we find A Ç B by looking for all the elements A and B have in common. We next illustrate with examples

To make it easy, notice that what they have in common is in bold

Let A = {

A Ç B = {1 orange, 1 apple}

Find the intersection of A and B and then make a Venn diagrams.

A = {

A Ç B = {4, b}

A = { x / x is a number bigger than 4 and smaller than 8}

B = { x / x is a positive number smaller than 7}

A = {

A Ç B = {5, 6}

Or A Ç B = { x / x is a number bigger than 4 and smaller than 7}

A = { x / x is a country in Asia}

B = { x / x is a country in Africa}

Since no countries in Asia and Africa are the same, the intersection is empty

A Ç B = { }

B = { }

This example is subtle! Since the empty set is included in any set, it is also included in A although you don't see it

Therefore, the empty set is the only thing set A and set B have in common

A Ç B = { }

In fact, since the empty set is included in any set, the intersection of the empty set with any set is the empty set.

Given three sets A, B, and C the intersection is the set that contains elements or objects that belong to A, B, and to C at the same time

We write A Ç B Ç C

Basically, we find A Ç B Ç C by looking for all the elements A, B, and C have in common.

A = {

A Ç B Ç C = {4 , # }

The graph below shows the shaded region for the intersection of two sets