Intersection and union of 3 sets

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Introduction
Lessons
  1. Introduction to Intersection and Union of 3 Sets:
  2. Intersection and Union of 3 Sets
  3. Principle of Inclusion and Exclusion with 3 Sets
Examples
Lessons
  1. Finding Intersection and Union of 3 Sets

    The Venn Diagram below shows the type of instruments that people like.

    Finding Intersection and Union of 3 Sets

    Find the following:

    1. n((D\cupG)\B)
    2. n((B\cupD)\G)
    3. n(D\capG\capB)
    4. n(D\G\B)
    5. n((D\capG)\cup(G\capB))
  2. Given the following Venn diagram:

    Find a, b, c.

    Circle A,B,A,B, and CC contain the same number of element. Find a,b,a,b, and cc .

    1. 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?

      1. 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?

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        Topic Notes

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

        n(A\cupB\cupC) = n(A) + n(B) + n(C) - n(A\capB) - n(B\capC) - n(A\capC) + n(A\capB\capC)