- Home
- Statistics
- Set Theory

# Intersection and union of 3 sets

- Intro Lesson: a12:32
- Intro Lesson: b8:07
- Lesson: 1a4:25
- Lesson: 1b1:56
- Lesson: 1c0:33
- Lesson: 1d1:14
- Lesson: 1e4:39
- Lesson: 211:41
- Lesson: 314:16
- Lesson: 49:46

### Intersection and union of 3 sets

#### Lessons

The principle of inclusion and exclusion of 3 sets says the following:

- Introduction
__Introduction to Intersection and Union of 3 Sets:__a)Intersection and Union of 3 Setsb)Principle of Inclusion and Exclusion with 3 Sets - 1.
**Finding Intersection and Union of 3 Sets**The Venn Diagram below shows the type of instruments that people like.

Find the following:

a)n((D$\cup$G)\B)b)n((B$\cup$D)\G)c)n(D$\cap$G$\cap$B)d)n(D\G\B)e)n((D$\cap$G)$\cup$(G$\cap$B)) - 2.Given the following Venn diagram:
Circle $A,B,$ and $C$ contain the same number of element. Find $a,b,$ and $c$ .

- 3.Richard surveyed 200 people to see which sports they like. Here is the information that Richard got:
- 70 people like soccer.

- 60 people like basketball.

- 50 people like tennis.

- 25 people like soccer and basketball, but not tennis

- 10 people like soccer and tennis, but not basketball.

- 7 people like basketball and tennis, but not soccer

- 10 people like all three sports

How many people don't like any of the sports?

- 4.
**Principle of Inclusion and Exclusion with 3 Sets**Willy surveyed 76 people for a cake shop. Each person ate at least one of the cakes: strawberry, chocolate and vanilla. Here is the information Willy got:

- 57 ate strawberry, 50 ate chocolate, and 39 ate vanilla.

- 20 ate both strawberry and chocolate, but not vanilla.

- 15 ate strawberry and vanilla, but not chocolate.

- 5 ate chocolate and vanilla, but not strawberry.

Who ate all three types of cakes?