# Intersection and union of 3 sets

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**Finding Intersection and Union of 3 Sets**The Venn Diagram below shows the type of instruments that people like.

Find the following:

- Given the following Venn diagram:
Circle $A,B,$ and $C$ contain the same number of element. Find $a,b,$ and $c$ .

- 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?

**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?