Intersection and union of 3 sets

All in One Place

Everything you need for better marks in university, secondary, and primary classes.

Learn with Ease

We’ve mastered courses for WA, NSW, QLD, SA, and VIC, so you can study with confidence.

Instant and Unlimited Help

Get the best tips, walkthroughs, and practice questions.

0/2
?
Intros
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
0/8
?
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?

        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)