Introduction to Sets
Some Exercises
1. List the members of the following sets.
a) {x | x is a real number such that x²= 4}
b) {x | x is an integer such that x² =2}
2. Determine whether each of the following pairs of sets is equal.
a. {1, 2, 1, 3, 1, 2}, {2, 3, 1}
b. {{1}}, {1, {1}}
c.
,{ }
3. For each of the follwoing sets, determine whether 1 is an element of that set.
a.
b.
c.
d.
e.
f.
{x R | x is an integer greater than 1}
{x R | x is the square of an integer}
{1, 2, {1}}
{{1}, {{1}}}
{{1, 2}, {1, {1}}}
{{{1}}}
4. Let A = {1, 2, 3, 4, 5, 6, 7}
Let C = {2, 4, 6, 8, 10}
Let B = { 1, 3, 5, 6}
Let D = {1, 2, 6, 7}
Write all the subset relations that exist between A, B, C, and D.
Find each of the following:
a) A C D
b) A B
c) D
d)
D
e) C
f)
C
B
B
C
D
 A D
A  C
g) C 
h)  D
C
D
5. Let A = {2, 3, 5, 7} Let B = {2, 4, 5, 6} Let C = { 12, 28, 35}
The set { 2, 5} is a subset of A. Using the subset symbol we can write this same fact
much more efficiently as 2,5  A .
Use the subset symbol to make a similar statement for each subset of A.
6. 4 is an element of B. Using the symbol for “is an element of” we can write this more
efficiently by writing 4  B .
Use the symbol for “is an element of” to make a similar statement about each element of
B.
7. What is A B ? How is it related to B? How is it related to A?
8. What is B C ? How is it related to B ? How is it related to C ?
9. What is A B ? How is it related to A ? How is it related to B ?