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SET THEORY

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SET THEORY

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  1. SET THEORY Chapter 2

  2. DAY 1

  3. Set – collection • School of fish • Gaggle of geese • Pride of lions • Pod of whales • Herd of elephants

  4. Set – usually named with a capital letter. • Well defined A is the set of the first three lower case letters of the English alphabet.

  5. Elements of the set A is the set of the first three lower case letters of the English alphabet. a, b, and c are elements of set A

  6. Natural Numbers (Counting Numbers) N = {1, 2, 3, . . . }

  7. Three ways of defining a set: • List A = {1,2,3} • Description A is the set of the first three counting numbers. • Set Builder Notation

  8. Universe • Empty set

  9. Example The set of natural numbers greater than 12 and less than 17.

  10. Example {x | x = 2n and n = 1, 2, 3, 4, 5}

  11. Example {3, 6, 9, 12, . . . }

  12. Example The set of the first 10 odd natural numbers.

  13. Venn Diagrams

  14. Set A

  15. Complement of A

  16. A intersect B

  17. A Union B

  18. Disjoint Sets

  19. Subsets A is a subset of B if every element of A is also an element of B.

  20. List all the subsets of {a,b,c} • { } • {a} • {b} • {c} • {a,b} • {a,c} • {b,c} • {a,b,c}

  21. List all the subsets of {a,b,c} • Proper Subsets: { } , {a} , {b} , {c} , {a,b} , {a,c} , {b,c} • THE Improper Subset: {a,b,c}

  22. Subset Notation Let A = {a,b,c} {a} A “The set of a is a subset of A.” (think: The set of a is a proper subset OR IS EQUAL TO A.) {a} A “The set of a is a proper subset of A.”

  23. True or False? A = {b,c,f,g} {b,f} A {b,f} A

  24. True or False? A = {b,c,f,g} {b,f} A True {b,f} A True

  25. True or False? A = {b,c,f,g} {b,d} A

  26. True or False? A = {b,c,f,g} {b,d} A False Because d A

  27. True or False? A = {b,c,f,g} {b,c,f,g} A

  28. True or False? A = {b,c,f,g} {b,c,f,g} A True {b,c,f,g} A

  29. True or False? A = {b,c,f,g} {b,c,f,g} A True {b,c,f,g} A False Because {b,c,f,g} = A

  30. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  31. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  32. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  33. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  34. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  35. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  36. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  37. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  38. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  39. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  40. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  41. U = {p,q,r,s,t,u,v,w,x,y,z}A = {p,q,r}, B = {q,r,s,t,u}, C = {r,u,w,y}

  42. DAY 2

  43. Homework QuestionsPage 83

  44. Three types of numbers. • Nominal • Ordinal • Cardinal “The student with ticket 50768-973 has just won second prize – four tickets to the big game this Saturday.”