1. College Algebra: Section 8.1 Sets and Counting Objectives of this Section Find All the Subsets of a Set Find All the Subsets of a Set Find the Intersection and Union of Sets Find the Intersection and Union of Sets Find the Complement of a Set Find the Complement of a Set Count the Number of Elements in a Set Count the Number of Elements in a Set

2. A set is a well-defined collection of distinct objects. Well-defined means there is a rule that enables us to determine whether a given object is an element of the set. If a set has no elements, it is called the empty set, or null set, and is denoted by the symbol

3. If two sets A and B have precisely the same elements, then A and B are said to be equal and write A = B.

4. Write down all subsets of {x, y, z}.

6. Example 2 n Let A={1, 3, 5, 8}, B={3, 5, 7}, and C={2, 4, 6, 8} and C={2, 4, 6, 8} n Find: n a. b. c.

8. U A B Venn Diagrams can be used to visually illustrate the set concepts discussed. U BA

9. U BA A U B A

10. U A A

12. Counting n If A is a set with n elements, then A has 2 n subsets. n Counting Formula:

13. In survey of 50 people, 21 said they owned stocks, 32 said they owned bonds and 12 said they owned both stocks and bonds. How many of the 50 people owned stocks or bonds? How many owned neither? A: person owns stock B: person owns bonds = 21 + 32 - 12 = 41 50 - 41 = 9 owned neither

14. Assignment n Page 699: 1-41 odds