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More lessons on Sets

Venn Diagrams

Intersection of Three Sets

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

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

To draw 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.

#### Venn Diagrams, Unions, and Intersections

Venn diagrams are an important tool allowing relations between sets to be visualized graphically.

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

**Union and Intersection of Sets**
#### Sets: Union, Intersection, Complement

Example:

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#### Sets: Union and Intersection

The basic idea of the 'union' and 'intersection' of two sets.

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.

More lessons on Sets

Venn Diagrams

Intersection of Three Sets

In this lesson, 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: **

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

**Solution: **

To draw 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 X ∩ Y = X**.

**Example: **

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

**Solution:**

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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