Ch 9 Inequalities and Absolute Value

1. Ch 9 Inequalities and Absolute Value 9.1 Sets, Intersection and Unions Goal(s): 1.) Name sets using set- builder and roster notation 2.) Find Intersections and Unions of sets

2. Wearing sweatshirt Blue eyes “Set” is a well-defined collection of objects called “members” or “elements”

3. Use pointed brackets List each element Three dots, called an ellipsis, indicate that the pattern continues forever, following the pattern set by the first 4 numbers. “Roster Notation” • The set of all whole numbers greater than 20 can be written: {21, 22, 23, 24, …}

4. Write using “roster notation” The set of all integers greater than 5 and less than or equal to 10 {6,7,8,9,10}

5. Write using “roster notation” The set of all prime numbers less than 12 {2,3,5,7,11}

6. List the first 4 Then write the ellipsis to show “the pattern continues” Write using “roster notation” The set of all positive odd numbers {1,3,5,7,…}

7. Write using “roster notation” The set of all positive multiples of 3 {3,6,9,12,…}

8. Description Means “such that” Set-builder Notation • Used to describe HOW a set is built, for example • {x|x is a whole number and x > 20}

9. Write using “set-builder notation” The set of all integers greater than 7 {x|x is an integer and x > 7}

10. Write using “set-builder notation” The set of all multiples of 5 that are less than 24 {x|x is a multiple of 5 and x < 24}

11. Use capital letters to name sets • “Z” is used to name the set of all integers • “Q” used for the set of all rational numbers €means “is an element of” And€means “isnotan elementof”

12. Let E be the set of even numbers True or False ?18 € E T

13. Let E be the set of even numbers True or False ?12 € E F

14. Write using “roster notation” and “set builder notation”: The set G of whole numbers greater than 5 G = {6,7,8,9,…} G = {x|x is a whole number and x>5}

15. Write using “roster notation” and “set builder notation”: The set T of multiples of 5 less than 24 T = {20,15,10,5,0,-5,…} T = {x|x is a multiple of 5 and x < 24

16. A B Intersection of two sets • Is the set of all members common to both sets. • Written A B (“A intersection B”) • Venn diagram representation:

17. 4 5 6 1 2 3 -2 -1 0 A B A = {1,2,3,4,5,6}B = {-2,-1,0,1,2,3}

18. 6 9 0 1 -3 -2 5 T P T = {0,1,6,9}P = {-3,-2,0,1,5}S = {-3,1,6}

19. T = {x|x is an even number}P = {y|y is an odd number}

20. A B Union of two sets • Is the set of all members either or both sets. • Written AB (“A union B”) • Venn diagram representation:

21. A B Union of two sets • Is the set of all members either or both sets. • Written AB (“A union B”) • Venn diagram representation:

22. 4 5 6 1 2 3 -2 -1 0 A B A = {1,2,3,4,5,6}B = {-2,-1,0,1,2,3}

26. Assignment:Page 403(2-42) even