1.         { } Sets and Venn Diagrams Prime Numbers Even Numbers
Odd Numbers       

2. SETS are named using a capital letter.
Sets A B C { }
A SET is a collection of objects. They can be numbers, words or things.
SETS are named using a capital letter.
Objects are listed inside brackets.
A = {2, 3, 5, 7, 11, 13}
B = {square, rectangle, trapezoid, rhombus, parallelogram}
C = {desk, chair, students, whiteboard, computer, teacher}

3. 7  A 10  A Element (of a Set)  
An ELEMENT of a set is a member of the set.
The symbol “” means “is a member of” and the symbol “” means “is not a member of”
7  A
A = {2, 3, 5, 7, 11, 13}
10  A

4. B  A C  A Subset (of a Set)  
A SUBSET of a set is a set that contains some or all of the elements of the set, but no other elements.
The symbol “” means “is a subset of” and the symbol “” means “is not a subset of”.
B  A
A = {2, 3, 5, 7, 11, 13}
B = {3, 5, 7}
C = {1, 2, 3, 4}
C  A

5. Subset (of a Set)   A B
B  A

6. A  B = {1, 2, 3, 4, 5, 6, 7, 9} Union (of 2 Sets) 
A UNION of 2 sets is a set that contains all of the elements of both sets.
Common elements are listed only once.
The symbol “” means “union of”.
A = {3, 5, 7, 9}
B = {1, 2, 3, 4, 5, 6}
A  B =
{1, 2, 3, 4, 5, 6, 7, 9}

7. Union (of 2 Sets) 
1, 2, 4
w, y, z A B x, 3
A = {1, 2, 3, 4, x}
B = {3, w, x, y, z}
A  B = {1, 2, 3, 4, w, x, y, z}

8. Intersection (of 2 Sets) 
An INTERSECTION of 2 sets is a set that contains only those elements that are in both sets.
The symbol “” means “intersection of”.
A = {3, 5, 7, 9}
B = {1, 2, 3, 4, 5, 6}
A  B = {3, 5}

9. Intersection (of 2 Sets) 
1, 2, 4
w, y, z A B x, 3
A = {1, 2, 3, 4, x}
B = {3, w, x, y, z}
A  B = {x, 3}

10. A  B = {} A  B =  Empty or Null Set {} 
An EMPTY OR NULL SET is a set that contains no elements.
The symbols “{} or ” stand for an empty or null set.
A  B = {}
A = {3, 5, 7, 9}
B = {2, 4, 6, 8} or
A  B = 

11. 1, 2, 3, 4 x, w, y, z B A A  B = {} or  Empty or Null Set {} 
B = {w, x, y, z}
A  B = {} or 

12. Complement A’
The COMPLEMENT of set A is all elements of the universal set, U, not in set A.
The Universal set will be defined for the situation.
The complement is denoted with a ’.
U = Odd numbers < 10
A = {1, 5, 9}
A’ = {3, 7}

13. A A’ = {8, 12, 24} Complement A’ U = Factors of 24 1, 2, 3, 4, 6

14. Description Notation (describes the set)
Additional Terms
Types of Set Notation:
Description Notation (describes the set)
I = the set of integers
A = the set of odd numbers less than 20
Roster Notation (lists the elements of the set)
I = {…, -3, -2, -1, 0, 1, 2, 3, …}
A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
Set Builder Notation (gives the property that defines each element)
I = {x|x is an integer}
A = {x|x is an odd whole number less than 20}

15. Infinite Set: a set whose elements cannot be counted or listed
Additional Terms
Infinite Set: a set whose elements cannot be counted or listed
I = {…, -3, -2, -1, 0, 1, 2, 3, …}
Finite Set: all elements can be counted or listed
A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}

16. Equivalent Sets: two sets that contain the same number of elements
Additional Terms
Equal Sets: two sets that contain the same elements but not necessarily in the same order
A = {c, 0, 1, d}
B = {d, 1, 0, c}
Equivalent Sets: two sets that contain the same number of elements
A = {1, 2, 3}
B = {4, 5, 6}