This is not a final presentation. This version is not peer reviewed and you should not cite it in scholarly writing.

1. Set operations with special thanks to Georg Cantor

2. Thank you for set theory Georg Cantor (1845 – 1918)

3. Founded set theory A single paper in 1874

4. Basic operations Binary relations and more

5. Fundamental relation An object o A set A

6. relation If o is an element of A, we write o ∈ A.

7. inclusion Let A be a set of all chihuahuas

8. inclusion Let B be the setof all dogs

9. inclusion All Chihuahuas are dogs.

10. inclusion A is a subset of B.

11. inclusion B is a superset of A.

12. Inclusion Subsets and supersets If all the members of set A are also members of set B, then A is a subset of B, denoted A ⊆ B.

13. union Union of two sets: A ∪ B

14. union denoted A ∪ B

15. Union of the sets A and B is the set of all objects that are a member of A, or B, or both.

16. Union The union of {1, 2, 3} and {2, 3, 4} is the set {1, 2, 3, 4} .

17. Intersection

18. intersection Intersection of three sets: A ∩ B ∩ C

19. intersection denoted A ∩ B

20. Intersection of the sets A and B is the set of all objects that are members of both A and B.

21. Intersection The intersection of {1, 2, 3} and {2, 3, 4} is the set {2, 3} .

22. complement Ac = U

23. complement The relative complement of A (left circle) inB (right circle):

24. complement denoted Ac

25. complement is the set of all members of U that are not members of A.

26. complement The complement of {1,2,3} relative to {2,3,4} is {4}

27. Cartesian product Direct product of two sets

28. Cartesian product denoted A × B

29. Cartesian product

30. Cartesian product of X and Y is the set whose members are all possible ordered pairs (x , y) where x is a member of X and y is a member of Y

31. Power set The set of all subsets of a set

32. Power set P(S) or ℘(S)

33. Power set If S is the set {x, y, z} the power set is P(S)={∅, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}

34. Power set the powerset of {1, 2} is { {}, {1}, {2}, {1,2} }

35. Attribution http://en.wikipedia.org/