Review for Exam 1 Solutions
Math 110
Complete the following exercises for a review. Questions on the exam will be similar to questions on
this review, questions from the homework assignments and the suggested exercises.
1. Use proper set notation and the listing method to express each as a set.
(a)
{−
1
,
0
,
1
,
2
,
3
,
4
}
(b)
{
4
,
8
,
12
,
16
}
(c)
{−
9
,
9
}
(d)
∅
2. Express each set using set builder notation.
(a)
{
x
:
x
≥
2 and
x
is even
}
(b)
{
x
:
x
is a perfect square between 1 and 36
}
(c)
{
x
:
x
is a day of the week
}
3. Determine
n
(
A
) for the following sets.
(a)
n
(
A
) = 9
(b)
n
(
A
) = 26
(c)
n
(
A
) = 4
4.
∅
,
{
1
}
,
{
2
}
,
{
3
}
,
{
1
,
2
}
,
{
1
,
3
}
,
{
2
,
3
}
,
{
1
,
2
,
3
}
5. Classify each of the following as true or false.
(i) true
6. Assume
A
=
{
1
,
2
,
7
,
8
,
9
}
,
B
=
{
2
,
4
,
6
,
8
}
and
C
=
{
5
,
7
,
9
}
. Let the universal set
U
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
,
9
}
.
Determine the following sets.
(k)
{
1
,
2
,
8
}
(l)
{
1
}
(m)
{
(5
,a
)
,
(7
,a
)
,
(9
,a
)
,
(5
,b
)
,
(7
,b
)
,
(9
,b
)
}
(n)
{
(
a,
5)
,
(
a,
7)
,
(
a,
9)
,
(
b,
5)
,
(
b,
7)
,
(
b,
9)
}
7. Show that the following sets are infinite by giving a one-to-one correspondence with a proper subset.