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Venn Diagrams

Venn Diagrams. Sets, Unions, Intersections, and Complements. Vocabulary Universe Element Set Subset Disjoint Mutually Exclusive Finite Infinite. Intersection Union Compliment Empty Set Cardinality A Priori Ad Hoc. Venn Diagrams. Venn Diagrams. Universe

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Venn Diagrams

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  1. Venn Diagrams Sets, Unions, Intersections, and Complements

  2. Vocabulary Universe Element Set Subset Disjoint Mutually Exclusive Finite Infinite Intersection Union Compliment Empty Set Cardinality A Priori Ad Hoc Venn Diagrams

  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

  4. 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

  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. A B 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. B A 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. B A C 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.

  13. 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, √2, etc. • Real numbers: R = Q + ~Q

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