Venn Diagrams

1
Venn Diagrams

• Sets, Unions, Intersections, and Complements

2
Venn Diagrams

• Vocabulary
• Universe
• Element
• Set
• Subset
• Disjoint
• Mutually Exclusive
• Finite
• Infinite

• Intersection
• Union
• Compliment
• Empty Set
• Cardinality
• A Priori
• Ad Hoc

3
Venn Diagrams

• Universe
• All of the items of interest
• Everything that could possibly occur
• Usually represented with a rectangle with or
  without a U
• Element symbol ?
• A single item in the universe
• In a list, elements are separated by commas

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Venn Diagrams

• Set
• A well defined group of elements within a
  universe
• Elements of the set are enclosed in a circle or
  in list form with braces m, a, t, h
• Subset symbol ?
• Any part or ALL of a of a set
• Proper Subset Contains zero or more elements of
  a set, but not ALL the elements m, a, t or t,
  a symbol ?
• Improper Subset Contains all of the same
  elements as the set itself m, a, t, h or h,
  a, m, t symbol ?

5
Venn Diagrams
Elements Proper Subsets Improper Subsets Total Subsets



6
Venn Diagrams

• Disjoint
• Two or more sets with no common elements
• Mutually Exclusive
• Two or more sets with no common elements
• Finite
• There are an exact number of elements
• Infinite
• Countably or un-countably unlimited number of
  elements

7
Venn Diagrams

• Intersection
• Elements common to two or more sets
• AND statements
• Symbol ?
• Union
• All elements present in two or more sets
  without repeats
• OR statements
• Symbol ?

8
Venn Diagrams

• Compliment
• Everything but the set itself
• The complement of A is written A
• Empty Set
• Contains no elements
• Symbol
• ?

9
Venn Diagrams

• Cardinality
• Number of elements in a set
• Cardinality of A is written n(A)
• A Priori
• Questions asked BEFORE research is done
• Ad Hoc
• Analyses performed AFTER research is done

10
Venn Diagrams

• What can you say about A and B?
• A Ç B Æ A È B A, B
• A and B are mutually exclusive or disjoint

11
Venn Diagrams

• What can you say about A and B?
• A Ç B A È B A Ç B
• A È B A Ç B A È B
• A Ç B A È B

12
Venn Diagrams

• What can you say
• about A, B, and C?
• A Ç B A È B
• A Ç C A È C
• B Ç C B È C
• A Ç B A È B
• A Ç B A È B Etc.

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Number sets

• Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Counting numbers N 1, 2, 3,
• Whole numbers W 0, 1, 2,
• Integers Z , -2, -1, 0, 1, 2,
• Rational numbers Q a/b, b ? 0, a, b ? Z
• Irrational numbers Q ?, e, v2, etc.
• Real numbers R Q Q