37.
B;
m
P
m
Q
m
R
¬
180
m
Q
m
Q
2(
m
Q
)
¬
180
4(
m
Q
)
¬
180
m
Q
¬
45
m
P
¬
m
Q
¬
45
38.
B; 4
x
y
5
x
¬
y
9
Page 100
Maintain Your Skills
39.
Let the four buildings be named
A
,
B
,
C
, and
D
. In
order to have exactly one sidewalk between each
building, there should be 6 sidewalks. If
AB
is the
sidewalk between buildings
A
and
B
, then the 6
sidewalks are
AB
,
AC
,
AD
,
BC
,
BD
, and
CD
.
40.
Valid; since 24 is divisible by 6, the Law of
Detachment says it is divisible by 3.
41.
Invalid; 27
6
4.5, which is not an integer.
42.
Valid; since 85 is not divisible by 3, the
contrapositive of the statement and the Law of
Detachment say that 85 is not divisible by 6.
43.
Sample answer: If people are happy, then they
rarely correct their faults.
44.
Sample answer: If you don’t know where you are
going, then you will probably end up somewhere
else.
45.
Sample answer: If a person is a champion, then
the person is afraid of losing.
46.
Sample answer: If we would have new knowledge,
then we must get a whole new world of questions.
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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Prime number, Inch, Metre, Kilometre

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