Relationships%20Between%20Sets

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• Relationships Between Sets

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Union

• Two people get married (union)
• and merge their DVD collections

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Union

• They sell all the duplicates on eBay.
• The DVDs that are left are the union of their
  collections. all of hers all of his dups

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Union

• Mathematically, we say that the number of
  elements in the union of two finite sets is
• the number of elements in Set A (his DVDs)
• PLUS the number of elements in Set B (her DVDs)
• MINUS the number of elements in the intersection
  of the sets (duplicates).
• N(AUB) n(A) n(B) n(A B)
• The DVDs that are left are the union of their
  collections. all of hers all of his dups

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Union

• Set A 1, 2, 3 Set B 3, 4, 5

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Intersection

• Just like the intersection of two roads,
• the intersection of two sets are the elements
  that are members of both sets.

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Intersection

• Set A 1, 2, 3 set B 3, 4, 5

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The empty set

• Set A 1, 2, 3 set B 4, 5, 6
• There is no element that is in both sets, so the
  intersection is the empty set.

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The empty set

• The symbol for the empty set is the Greek letter
  Phi
• Do not put it in brackets.

is not empty. It is a set with one element
the Greek letter Phi
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Venn Diagrams

• One way to graphically represent sets is by using
  Venn diagrams.
• John Venn (1834 1923), was a British logician
  and philosopher who introduced the Venn diagram,
  which is used in many fields, including set
  theory, probability, logic, statistics, and
  computer science.

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Universal Set

• To use a Venn diagram, you must first start with
  a universal set, represented by U, which contains
  all of the elements being considered in a
  problem.
• In a problem about Chevys and Fords, the
  universal set might be the set of all cars.

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Venn Diagram

• If U all cars and F all Fords, the Venn
  diagram would look like this
• Its easy to see that F is a proper subset of U.
  F U

U
F
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Venn Diagram

• The complement of F is the set that consists of
  all of the members of U that are not in F (the
  green area)
• The complement of F is written F.

U
F
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Venn Diagram

• If U all cars, and F all Fords, and C
  all Chevys the Venn diagram would look like
  this
• Its easy to see that both F and C are subsets of
  U.

U
F
C
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Disjoint Sets

• In this case, the sets are disjoint - meaning
  that they dont overlap.

U
F
C
There are no cars that are both Fords and Chevys
- my neighbor sort of has one, but thats a long
story
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Vocabulary
Element Subset Union Intersection Empty set