1. Sets and Operations
TSWBAT apply Venn diagrams in problem solving; use roster and set-builder notation; find the complement of a set; apply the set operations of intersection and union; identify a disjoint set

2. Think about it – How would you go about finding out this answer?
Of 250 people surveyed, 175 have brown hair, 110 have brown eyes, and 85 have both brown hair and brown eyes. How many of these people have neither brown hair nor brown eyes?

3. Venn Diagrams Venn diagrams show relationships between sets Set
A collection of objects, called elements
Elements
Numbers, letters, or physical objects
They are written between braces {}
Two sets are equal ONLY if they have the exact same elements

4. Drawing Venn Diagrams Universe Subsets
The set of all elements being considered
Illustrated by a rectangle
Subsets
A set contained within a set
Denoted by the symbol
Illustrated as circles within the rectangle U

5. Use a Venn diagram
110-85
175-85 85 90 25 U U 50
This blue rectangle is the universe U = 250

6. Different Notations Roster notation
List the elements of a set in brackets
Example
The set of whole numbers greater than 10
{11, 12, 13, 14…}
… or a ellipsis is used to show that the set continues without end following the established pattern

7. Different Notations Set-builder notation
Describes the set by stating the properties that its elements must satisfy
Example
The set of whole numbers greater than 10
{x|x is a whole number and x > 10}
Read as: the set of all x such that x is a whole number and x is greater than 10

8. Symbols used Є Read as “is an element of”, or “belongs to”
50 Є {x|x is a whole number and x>10}
Read as “is not an element of” or “does not belong to”
7 Є {x|x is a whole number and x>10}

9. Empty Sets
A set that has no elements is called and empty set or a null set
It can be denoted two ways {} Ø
Do NOT write 0, zero is a number and empty set does not contain zero as an element

10. Examples List the elements of each set
{q|q is a whole number and q<0} {}
{t|t is an integer and t<0}
{…, -4, -3, -2, -1}
{v|v Є the set of integers and v>0}
{21, 22, 23…}
{n|n Є the set of natural numbers and n<0} Ø

11. Classwork Complete numbers 1-4 on page 19 of your workbook
Turn it in when you are finished

12. Complements When a subset is defined, its complement is also defined
The complement is denoted by the’ symbol
Set A
Complement is A’
Complement
The set of all elements in the universe (U) but do not belong to the set

13. Examples
If U = {0, 1, 2, 3, 4 ] and A = {0, 1, 3}, what is the complement of A?
A’ = {2, 4}
U = {integers}, A = {0}
{… -3, -2, -1, 1, 2, 3…}
U = {real numbers}, A = Ø
A’ = {real numbers}

14. Example
U = {1, 2, 3}, A = {1, 2, 3}
A’ = {}
In your workbook complete page 19, 5-10

15. Operations with sets Intersection of sets U U U
The elements BOTH sets contain
Denoted with the symbol U U U

16. Example of Intersection
B = {2, 5, 6, 7}
A B = {2, 5} U

17. Operations with Sets Union of Sets U U U U
All elements that are in either or both sets
Denoted by the symbol U U U U

18. Example of Union A = {1, 2, 3, 4, 5} B = {2, 5, 6, 7}
A U B = 1, 2, 3, 4, 5, 6, 7}

19. Examples A U B A C B U C A B C A (B U C) A U (B C) U U U U U A 20 8 79 U 4 2 3 B C

20. Classwork
Complete WB page 20, 11-18