Operations with sets

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Operations with sets

  1. 1. Set Operations & Cartesian Products
  2. 2. Unions
  3. 3. Examples; Unions of Sets
  4. 4. Intersections
  5. 5. Examples; Intersection of Sets
  6. 6. Difference ofSets
  7. 7. Examples; Difference of Sets
  8. 8. Ordered PairsOrder Matters! Different than sets  In sets, it does not matter what order the elements are in  Ordered pairs are equal only if both first components are the same and both second components are the same
  9. 9. Cartesian ProductsNamed after Rene Descartes• Formulated analytic Geometry• French Philosopher• “I think, therefore I am”
  10. 10. Cartesian Products of Sets
  11. 11. End of Day 1
  12. 12. Cartesian Products “ORDER MATTERS”
  13. 13.  The order in which the sets areFindingCartesian listed matters.products  First component is always from set A  Second component is always from Set B  Example N= {4, 3, 2} T = {1, 5}  Find the Cartesian Product N x T  Pair each element of N with each element of T  {(4,1), (4,5), (3,1), (3,5,), (2,1,), (2,5)}
  14. 14. Example: Cartesian Product of a set with itself• Let Z = {5, 9, 3, 6}• Find Z x Z • {(5,5), (5,9), (5,3), (5,6), (9,5), (9,9), (9,3), (9,6), (3,5),(3,9), (3,3), (3,6), (6,5), ( 6,9), (6,3), (6,6)}
  15. 15.  Multiply together the cardinalCardinalNumbers of numbers for each set, to find theCartesian Cardinal Number (total # ofProducts elements) in the Cartesian Setn(A) • n(B)Let n(A) = a  Order of sets doesn’t changeLet n(B) = b cardinal number of the Cartesian Products  n(A) • n(B) = n(B) • n(A)
  16. 16. Cardinal Number of Cartesian Products• P = {2,5,7} Q = {8, 9, 10}• FIND P X Q • {(2,8), (2,9), (2,10), (5,8), (5,9), (5,10), (7,8), (7,9), (7,10)} • n(P x Q) = 9 • n(P) =3 and n(Q) = 3 • n(P) • n(Q) = 9• FIND Q X P • {(8,2), (8,5), (8,7), (9,2), (9,5), (9,7), (10,2), (10,5), (10,7)} • n(Q x P) = 9
  17. 17. Venn DiagramsREPRESENT SET OPERATIONS WITH VENN DIAGRAMS • COMPLIMENT • INTERSECTION • UNION • DIFFERENCE • CARTESIAN PRODUCT
  18. 18. SameSame
  19. 19. f gU A B a b d e c

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