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# SET THEORY

## SET THEORY

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##### Presentation Transcript

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. DAY 2

31. Homework QuestionsPage 83

32. 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.”