Notes for Lesson 3-8: Unions and Intersections of Sets

3-8.1 –Unions of Sets

Vocabulary:

Union – The set that contains all the elements of two or more sets.

Intersection – The set of elements that are common to every set.

Disjoint Sets – Sets that have no elements in common

If you are given two or more sets, you can describe which of the elements belong to at least one set. The union of a set is all of the elements that are members to either set. The symbol for union is .

A B

Examples:

If then because they are all the different elements in both A and B.

If your left pocket has in it a Quarter, a paper clip and a key, and your right pocket has a penny, quarter, and a pencil. Then the union of your pockets would be a quarter, paper clip, key, penny and pencil.

If then

3-8.2 – Intersections of a set

If you are given two or more sets, every element that is in the sets is called the intersection of those sets.

The symbol for intersection is .

Examples:

If then because they are all the elements in both A and B.

If your left pocket has in it a quarter, a paper clip and a key, and your right pocket has a penny, quarter, and a pencil. Then the intersection of your pockets would be a quarter because it is the only thing in both pockets.

If then

3-8.3 – Disjoint Sets

Sets that do not have any elements in common are called disjointed sets

3-8.4 – Making a Venn diagram

Three friends go camping. One has a yellow pack with a flashlight, pan, water sunglasses hat and map. One has a red pack with a pan water rope first aid kit hat and map, The third has a blue pack with water hat map first aid kit and a camera.

Yellow Red

Flashlight PanRope

Sunglasses

Water

Hat

Map first sid

kit

Camera

Blue

You see the equipment that is in all three bags is the intersection.

3-8.5 – Using Venn diagrams to show number of elements

You can use Venn diagrams to also find the number of elements.

Example: Of 500 commuters polled, some drive to work, some take the bus and some do both. 200 Commuters drive to work and 125 use both, Find the number of commuters who use the bus.

Drive Bus

200 total Both

500-200=300

200-125=75125 300 bus ridersso 300 bus + 125 both = 425 who ride bus