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More lessons on Sets

Venn Diagrams

Intersection of Three Sets

In these lessons, we will learn how to use Venn Diagrams to illustrate the intersection of two sets.

More lessons on Sets

Venn Diagrams

Intersection of Three Sets

In these lessons, we will learn how to use Venn Diagrams to illustrate the intersection of two sets.

The **intersection** of two sets *X* and *Y* is the set of elements that are common to both set *X* **and** set *Y*. It is denoted by *X* ∩ *Y* and is read ‘*X* intersection *Y* ’.

**Example: **

Draw a Venn diagram to represent the relationship between the sets

*X* = {1, 2, 5, 6, 7, 9, 10} and *Y* = {1, 3, 4, 5, 6, 8, 10}

**Solution: **

We find that *X* ∩ *Y* = {1, 5, 6, 10} ← in both *X* and *Y *

For the Venn diagram,

** Step 1** : Draw two overlapping circles to represent the two sets.

** Step 2** : Write down the elements in the intersection.

** Step 3** : Write down the remaining elements in the respective sets.

Notice that you start filling the Venn diagram from the elements in the intersection first.

**If *** X *** ⊂ Y then**

We will illustrate this relationship in the following example.

**Example: **

Draw a Venn diagram to represent the relationship between the sets

* X* = {1, 6, 9} and *Y* = {1, 3, 5, 6, 8, 9}

**Solution:**

We find that *X* ∩ *Y* = {1, 6, 9} which is equal to the set *X*

For the Venn diagram,

** Step 1** : Draw one circle within another circle

** Step 2** : Write down the elements in the inner circle.

** Step 3** : Write down the remaining elements in the outer circle.

This video introduces the use of Venn diagrams to visualize intersections and unions of sets, as well as subsets and supersets.

U = {7,8,9,10,11,12,13}

A = {8,10,12}, B = {10,12,13}, C = {7,8}

Find

A ∪ B

A ∩ B

A ∪ B'

(A ∪ B') ∩ C

The intersection of two sets are those elements that belong to both sets.

The union of two sets are all the elements for both sets.

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