RED
Name:
Instructor: Pace Nielsen
Math 290
Sample Exam 3
Note that the first 10 questions are truefalse. Mark A for true, B for false. Questions 11
through 20 are multiple choice–mark the correct answer on your bubble sheet. Answers to
the last five questions should be written directly on the exam, and should be written neatly
and correctly.
Truefalse questions
1. Let
A
be an uncountable set. There is no uncountable set

B

with

B

<

A

.
2. A set
A
is countable if and only if there is a bijection
f
:
N
→
A
.
3. Every subset of an uncountable set is either finite or denumerable.
4. For every nonempty set
A
the sets
P
(
A
) and
{
0
,
1
}
A
are numerically equivalent.
5. Let
S
=
{
(
a, b
)
∈
N
×
N
:
a
≤
b
2
}
. Then
S
is denumerable.
6. If
A
and
B
are nonempty sets, then

A
×
B
 ≤ 
A

.
7. Let
p
∈
Z
with
p
≥
2. Then
p
is prime if and only if for all
a
∈
Z
, either
p

a
or (
a, p
) = 1.
8. Suppose that
n, d, q, r
∈
Z
with
n, d
6
= 0 and
n
=
qd
+
r
. Then gcd(
n, d
) = gcd(
d, r
).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Smith
 Math, Countable set, Georg Cantor, Uncountable set

Click to edit the document details