3.1/
15, 10, 22, 23, 37, 41, 50
1. Let
S
= {2, 5, 17, 27}.
Which of the following are true?
a. 5
œ
S
b. 2 +5
œ
S
c. {}
œ
S
d.
S
œ
S
Note that 2 + 5 = 7, which is not in
S
.
There are no sets that are elements of
S
, so {} and
S
can't be in
S
2. Let
B
= {
x  x
œ
and 1 <
x
< 2}.
Which of the following are true?
a. 0
œ
B
b. 1
œ
B
c. 0.84
œ
B
d.
◊
2
œ
B
Note that 1 is not less than 1, and that
◊
2 is not in
3. How many different sets are described in the following?
What are they?
{2, 3, 4}
set
A
{
}
set
B
{
x  x
is the first letter of cat, bat or apple}
set
C
{
x  x
is the first letter of cat, bat and apple}
set
B
{
x  x
œ
N
and 2 <=
x
<= 4}
set
D
{2,
a
, 3,
b
, 4,
c
}
set
E
{a, b, e}
set
F
{3, 4, 2}
set
D
Note that since no letter can be the first letter of cat, bat and apple, that set is empty.
4. Describe each of the following sets by listing its elements:
a. {
x  x
œ
and
x
2
< 25}
{0, 1, 2, 3, 4}
b. {
x  x
œ
and
x
is even and 2 <
x
< 11}
{4, 6, 8, 10}
c. {
x  x
is one of the first three presidents of the United States}
{Washington, Adams, Jefferson}
d. {
x  x
œ
and
x
2
= 1}
e. {
x  x
is one of the New England states}
{Maine, Vermont, New Hampshire, Massachusetts, Rhode Island, Connecticut}
f. {
x  x
œ
and 
x
 < 4}
{3, 2, 1, 0, 1, 2, 3}
5. Describe each of the following sets by listing its elements:
a. {
x  x
œ
and
x
2
– 5
x
+ 6 = 0}
{2, 3}
b. {
x  x
œ
and
x
2
= 7}
{}
c. {
x  x
œ
and
x
2
 2
x 
8 = 0}
{4}
(note that 2 is not in
)
10. Let
A
= {
x  x
œ
and 1 <
x
< 50},
B
= {
x  x
œ
and 1 <
x
< 50},
C
= {
x  x
œ
and
x

¥
25}
Which of the following statements are true?
a.
A
Œ
B
b. 17
œ
A
c.
A
Œ
C
5 is in
A
, but not in
C
d. 40
œ
C
e.
◊
3
œ
B
f. {0, 1, 2}
Œ
A
0 is not in
A
g. {}
œ
B
I don't see any empty sets listed as an element of
B
, do you?
h.{
x  x
œ
Z and
x
2
¥
625}
Œ
C
22. Find
P
(S) for
S
= {1, 2, 3, 4}.
How many elements do you expect to have?
We would expect 2
4
subsets.
They are: {}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, .
.. ,
{1, 2, 3, 4}.
23. Find
P
(S) for
S
= {
f
}.
P
({
f
}) = {{}, {
f
}}