1. OTCQ 09/14/09 Define point and plane.

2. Aim 1-1 part 2 How do we use set and interval notation, and find a complement of a set? NY AA 29 and AA 30

3. Aim 1-1 Standards (NO WRITE) A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form A.A.30 Find the complement of a subset of a given set, within a given universe

4. Aim 1-1 Objectives(Please write) SWBAT 1.Use { and } to write sets as lists aka rosters in set builder form. 2.Translate from,, open circles, closed circles, set interval notation ( ) and[ ]. 3.Understand complement means anything not included in the set but still in the universe. 4.Understand that the universe is everything of that kind.

5. OBJ#1Sets and set notation A set is a collection of objects called the elements or members of the set. Set braces { } may be used to list the elements of a set. Example {1,2,3} Translated {1,2,3} means the set of numbers including 1, 2 and 3 This is referred to as a Finite Set since we can count the elements of the set.

6. Sets and set notation Example : N= {1,2,3,4,…} is referred to as the Natural Numbers or Counting Numbers Set. Example : W= {0,1,2,3,4,…} is referred to as the Whole Number Set. What does... mean? Can you recall the other number sets?

7. I – Integer numbers: {…,-2, -1, 0, 1, 2, …} R - Rational numbers (repeating decimals and fractions). IR – Irrational numbers: (can’t be expressed as fractions, decimals that never repeat). Any questions about set braces { and }?

8. OBJ 2 First, lets recall how to graph inequalities on a number line. Then we will connect this knowledge to the description of a set of numbers. Go to: http://www.phschool.com/atschool/acad emy123/html/bbapplet_wl-problem- 430715.html

9. The number line represented by x > 5 is a set. In words x > 5 means the set of all numbers greater than or equal to 5. What is the greatest number in that set? Would it be convenient to list all the numbers between { and }?

10. Rules for translating from inequalities to number lines and then to set interval notation. 1. go with open circles and ( and ). 2. go with closed circles and [ and ]. Next, connecting number lines and set interval Notation.

11. Ex: 5 < x < 10 For this example think of only natural numbers! We will 1.Graph this on a number line. 2.Translate this to words that describe a set. 3.Translate this to set interval notation.

12. 5 < x < 10 Please 1.Graph this on a number line. 2.Translate this to words that describe a set. 3.Translate this to set interval notation. <5<5 < 10 Notice that based on the rules I chose an open circle for 5 and a closed circle for 10?

13. 5 < x < 10 Please 1.Graph this on a number line. 2.Translate this to words that describe a set. 3.Translate this to set interval notation. 5 10 In words, the number line describes the set of numbers greater than 5 and less than or equal to 10.

14. 5 < x < 10 Please 1.Graph this on a number line. 2.Translate this to words that describe a set. 3.Translate this to set interval notation. <(5<(5 < ] 10 (5,10] = Set Interval notation. Notice that < and ( go together and < and ] go together. This also means the numbers greater than 5 and less than or equal to 10.

15. 5 < x < 10 could als be listed in braces as {6,7,8,9,10} Using only natural numbers.

16. Summary so far objs 1 & 2:  5 < x < 10 can be expressed as a number line graph.  5 < x < 10 can be translated as (5,10].  5 < x < 10 can be translated as {6,7,8,9,10}. 5 10

17. You try: -3 < x < 4 Please (we try together) 1.Graph this on a number line. 2.Translate this to words that describe a set. 3.Translate this to set interval notation.

18. One for you: -3 < x < 4 Please 1.Graph this on a number line. 2.Translate this to words that describe a set. 3.Translate this to set interval notation. -3 4

19. One for you: -3 < x < 4 Please 1.Graph this on a number line. 2.Translate this to words that describe a set. 3.Translate this to set interval notation. -3 4 #2: The set of numbers greater than or equal to -3 and less than 4.

20. One for you: -3 < x < 4 Please 1.Graph this on a number line. 2.Translate this to words that describe a set. 3.Translate this to set interval notation. -3 4 [-3,4)

21. How could we write x < -2? Does < go with ( and ) or [ and ]?

22. How could we write x < -2 With set interval notation? < goes with ( and ). But try a number line first just so you see what else has to go in the interval notation.

23. x < -2?  < goes with ( and ), but the number line arrow points left which means we are headed for - . So we write , [- , -2) In words this means? Why did I use a bracket for - infinity? Because the [ implies equal to. Always use a bracket next to infinity.

24. How could we write x < -2 with { and }? {... -5, -4, -3, -2} This is probably the best for this example. We have several ways to describes sets because we like to choose the simplest.

25. OBJ 3 Venn Diagrams, Complements and Subsets  Set B is called a subset of the set A if all of Set B (blue area) is contained in Set A (Green area)  B ⊂A A  The complement of Set B within Set A means anything outside of Set B and still within set A.  Can you think of any examples of sets, subsets and complements? OTCQ Tuesday. Like: What is the complement of Queens in NYC? B A

26. Aim 1-1 Objectives Check back(no write) SWBAT check. Can you? Let’s look at our worksheet/homework? 1.Use { and } to write sets as lists aka rosters in set builder form. 2.Translate from,, open circles, closed circles, set interval notation ( ) and[ ]. 3.Understand complement means anything not included in the set but still in the universe. 4.Understand that the universe is everything of that kind.

27. Xc?Union  The union of two sets A and B is the set of all elements x such that x is in A OR x is in B  Notation: A ∪ B A B A ∪ B

28. Intersection  The intersection of two sets A and B is the set of all elements x such that x is in A AND x is in B  Notation: A ∩ B A B A ∩ B