Sets and Set Operations

1. Sets and Set Operations

2. Objectives • Determine if a set is well defined. • Write all the subsets of a given set and label the subsets as proper or improper. • Given a universal set and some subsets, find a complement, intersection or union. • Draw a Venn diagram to illustrate two sets. • Use the cardinal number formula.

3. Vocabulary • roster notation • set-builder notation • well defined set • cardinal number • empty set • subset • proper/improper subset • intersection of sets • union of sets • mutually exclusive • complement of a set

4. Set Vocabulary: roster notation: a complete or implied listing of all the elements of the set set builder notation: used when the roster method is cumbersome or impossible

5. Set Vocabulary: well defined set: A set is well-defined if any given object either is an element of the set, or is not an element of the set

6. Determine if the given set is well defined. The set of all good bands The set of odd numbers The set of small numbers - not well defined - well defined - not well defined

7. Symbols related to sets:

8. Symbols related to sets:

9. Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2, 4, 5, 6, 8}, andB = {1, 3, 5, 7}Answer the questions below: • Find n(B). • Find the set A B. • Find the set n(B) = 4 A  B = {5} These are the things that are in set A and also in set B at the same time. = {0, 2, 4, 6, 8, 9} These are the things that are in set U (the universe for our problem) that are not in set B.

10. Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2, 4, 5, 6, 8}, andB = {1, 3, 5, 7}Answer the questions below: • Find the set . • Is 7A true or false? • Is 5B true or false?

11. Formulas Cardinal Number Formula for the Union of Sets n(AB) = n(A) + n(B) — n(AB) Cardinal Number Formula for the Complement of a Set

12. Suppose n(U) = 61, n(A) = 32, and n(B) = 26. If n(AB) = 40, find n(AB) and draw a Venn diagram to illustrate the composition of U. n(AB) = n(A) + n(B) — n(AB)

13. In a recent health survey, 750 single men in their twenties were asked to check the appropriate box or boxes on the following form. I am a member of a private gym. I am a vegetarian. The results were tabulated as follows: 374 checked the gym box 92 checked the vegetarian box 332 were blank (no boxes checked)

14. 750 men surveyed 374 checked the gym box 92 checked the vegetarian box 332 were blank (no boxes checked) • Draw a Venn diagram illustrating the results of the survey. • What percent of these men were both members of a private gym and vegetarians.

15. Cards

16. Cards Determine how many cards, in an ordinary deck of 52, are clubs or twos.

17. Cards Determine how many cards, in an ordinary deck of 52, are face cards or diamonds.

18. Cards Determine how many cards, in an ordinary deck of 52, are threes or sixes.

19. Cards Determine how many cards, in an ordinary deck of 52, are threes and sixes.