1. 3.5 SETS Roster Form: use the { } to list the elements of the set ex: { 1, 2, 3, 4, 5, 6, 7, 8, 9} Set Builder Notation: use the { } to describe the properties of the elements of the set ex: { x | 1 < x < 9 } Empty Set (Null Set): set that contains no elements ex: { },

2. Subset ( ): the list of some or all the elements in a set. Ex: A = { x |0 < x < 9 } Some subsets are: B = {1} C = {1,2} D = {1,2,3} E = {1,2,3,4},,, etc. Universal Set: the largest set we are using Ex: { x | x is an element of the real numbers}

3. Complement of a Set (A’): the set of all elements in the universal set that are not in the set. Ex: A = { x |0 < x < 9 } B = { x | multiple of 2 and < 9} B’ = { 1, 3, 5, 7 }

4. GOAL:

5. RATIONALS : Any number that can be written in fraction form 3, 1/3, -5, -1/5, 1+(2/3), …. INTEGERS: Naturals and Whole and Negative numbers. …-3,-2,-1,0,1,2,3,….. WHOLE NUMBERS: Naturals and 0 0,1,2,3,…… NATURAL NUMBERS: Numbers we use to count items. 1, 2, 3, 4,…….. REMENBER THE REAL NUMBERS

6. REAL-WORLD: Let the Universal set U = {planet’s in Earth’s solar system} and set P = {planets farther from the sun than earth is from the sun}. What is the complement of set P? Write the answers in both forms.

7. SOLUTION: Remember that the complement of a set are the elements that are not on that set. U = { Mars, Jupiter, Saturn, Uranus, Neptune, Mercury, Earth, Venus} P = { Mars, Jupiter, Saturn, Uranus, Neptune} COMPLEMENT (P’): Elements not in P P’ = {Mercury, Earth, Venus}

8. YOU TRY IT: Let U = {days of the week} A = { days of the week with letter N} a)What are the elements of U? b)What are the elements of A? c)How do you find A’?

9. SOLUTION: a) U = { Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} b) A = { Sunday, Monday, Wednesday} c) To find A’ we look for the elements that are in U but not in A: { Tuesday, Thursday, Friday, Saturday}

10. VIDEOS: Sets Sets of Numbers: http://www.khanacademy.org/math/probability/in dependent-dependent- probability/basic_set_operations/v/relative- complement-or-difference-between-sets http://www.khanacademy.org/math/probability/in dependent-dependent- probability/basic_set_operations/v/universal-set- and-absolute-complement

11. CLASSWORK: Page 197-198: “DO AS MANY PROBLEMS AS IT TAKES FOR YOU TO MASTER THE CONCEPT!!!”