Intersection and union of 3 sets

Intersection and union of 3 sets

Lessons

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)

  • Introduction
    Introduction to Intersection and Union of 3 Sets:
    a)
    Intersection and Union of 3 Sets

    b)
    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.

    Finding Intersection and Union of 3 Sets

    Find the following:

    a)
    n((D\cupG)\B)

    b)
    n((B\cupD)\G)

    c)
    n(D\capG\capB)

    d)
    n(D\G\B)

    e)
    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 .


  • 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?