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M325K
HW 05  Solutions to Graded Questions
(Out of 25 points)
Section 3.2
10.
(4pts)
Since
m
and
n
are integers,
n
m
12
5
+
and
n
4
are both integers (sums and products of integers are
integers). Also since
0
≠
n
, we have
0
4
≠
n
. Thus
n
n
m
4
12
5
+
is a quotient of integers with a nonzero
denominator. Hence, it is rational.
22.
(4pts) True.
Proof.
Suppose
k
is any even integer and
m
is any odd integer. Then
2
+
k
is even by property 1 on p.145.
Also
2
)
2
(
+
k
is even because it is product of two even integers (again by property 1).
Since
m
is odd,
1
−
m
is even by property 2. Thus
2
)
1
(
−
m
is even by property 1 because it is a product of
two even integers. Finally
2
2
)
1
(
)
2
(
−
−
+
m
k
is even because it is a difference of two even integers (this is
property 1).
35.
(3pts) This incorrect “proof” begs the question by assuming what is to be proved. Namely, the forth
sentence claims that
s
r
+
is a fraction because it is a sum of two fractions. But this is a restatement
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 Spring '10
 seckin
 Integers

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