RED
Name:
Instructor: Pace Nielsen
Math 290
Sample Exam 2
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
R
be an equivalence relation on a nonempty set
A
, and let
a, b
∈
A
. Then [
a
] = [
b
] if
and only if
aRb
.
2. If

A

= 1 and
R
is a reflexive relation on
A
, then
R
is an equivalence relation.
3. If
f
:
A
→
B
is injective, and
g
:
B
→
C
is surjective, then
g
◦
f
:
A
→
C
is bijective.
4. If
R
is an equivalence relation on a finite nonempty set
A
, then the equivalence classes of
R
all have the same number of elements.
5. Let
A
be a set and let
R
be an equivalence relation on
A
. Suppose that
a
and
b
are in
A
,
that there are exactly eight elements
x
such that
xRa
and there are exactly nine elements
y
such that
yRb
. Then it is possible that
aRb
.
6. Let
A
=
{
a, b, c, d
}
and let
R
be an equivalence relation on
A
. Suppose that
aRb
,
cRd
, and
dRc
. Then it must be the case that
aRd
.
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 Spring '11
 Smith
 Math, Equivalence relation, Binary relation, Inverse function

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