Intersection and union of 3 sets

Lessons

• 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
  
  

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• 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))
  
  

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• 2.
  Given the following Venn diagram:

  

  Circle $A,B,$ and $C$ contain the same number of element. Find $a,b,$ and $c$ .

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• 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?

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• 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?

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