LET’S TALK ABOUT SETS
(Sets and Venn Diagrams)
SET:
UNIVERSAL SET (S):
SUBSET ():
 a group of items called elements or members
 ex. A = {1, 2, 3, 4, 5}
 3  A “3 is an element of set A”
 the set containing ALL elements being
considered
 a set whose elements are also elements of
another set
 ex. if all elements of set C are also elements of
set A then C  A
 every set is a subset of itself
EMPTY (NULL) SET:  a set that contains NO elements
 denoted using { } or 
VENN DIAGRAM:
 depicts relationships among sets
 named after the logician, John Venn (1834-1923)
S
S
A
Subset: A  S
Universal Set
S
S
A
B
Intersection: A  B
“and”
 set A and B contain
COMMON elements
A
B
Union: A  B
“or”
 elements belong to
set A or set B
Example 
List all subsets of the set A = {1, 3, 5}.
Example 
Given the sets, A = {2, 4, 6, 8} and B = {1, 2, 3, 4}, list the
elements of each of the following:
a) S =
b) A  B =
c) A  B =
d) A  S =
Example 
List the elements in each of the following sets:
a) {x  3 < x ≤ 8, x  N } =
b) { factors of 12 } =
SETS: The Basic Concepts
(Worksheet)
1.
List the members of each of the following sets:
a)
b)
c)
d)
e)
the set of vowels in the English language
the set of positive odd integers less than 10
the set of months beginning with the letter J
{ x  1  x  7, x  N }
the set of real numbers x, for which x2 = –1
2.
Give all the subsets of {3,6}.
3.
Which of the following statements are true?
a)
b)
c)
d)
e)
f)
4.
Let A = {3, 8, 12, 16, 19}, B = {0, 1, 3, 4, 7}, C = {8, 12, 19}, and D = {8, 12}.
a)
b)
5.
List all pairs of sets in which one is a subset of the other.
List all pairs of sets such that one is not a subset of the other.
List the elements in each of the following sets:
a)
b)
c)
6.
3  {2, 3, 4, 5}
5  {1, 3, 5, 7, 9}
{1, 2, 3} = {3, 1, 2}
the set of all natural numbers less than 5 is {1, 2, 3, 4}
{ x  x  6, x  N } = {1, 2, 3, 4, 5}
7 is a member of the set of odd whole numbers
{ one-digit even whole numbers }
{ factors of 24 }
{ prime numbers between 10 and 50 }
Write a description of each of the followings sets:
a)
{1, 5, 10, 25, 100, 200}
b)
{2, 3, 5, 7, 11, 13}
ANSWERSANSWERSANSWERS
1.a)
d)
2.a)
3.a)
e)
4.a)
5.a)
6.a)
b)
{a,e,i,o,u}
b) {1,3,5,7,9}
c) {January, June, July}
{2,3,4,5,6,7}
e) { }
{ }, {3}, {6}, {3,6}
true
b) false
c) true
d) true
false
f) true
C  A, D  A, D  C
b) (A,B), (B,C), (B,D)
{2,4,6,8}
b) {1,2,3,4,6,8,12,24}
c) {11,13,17,19,23,29,31,37,41,43,47}
the set of Canadian coin values
the set of natural prime numbers less than or equal to 13