1
CHAPTER R
Section R1
1.
True
3.
False
5.
False
7.
True
9.
False
11.
True
13.
1
15.
Division by zero is not defined. Undefined.
17.
0 ÷ (9·8) = 0 ÷ 72 = 0
19.
0 ·
100
+
1
100
±
²
³
´
µ
¶
= 0 since
a
·0 = 0·
a
= 0 for all real numbers
a
.
21.
4
9
+
12
5
=
4
±
5
+
12
±
9
9
±
5
=
20
+
108
45
=
128
45
23.

1
100
+
4
25
±
²
³
´
µ
¶
= 
1
100
+
16
100
±
²
³
´
µ
¶
= 
17
100
or
±
17
100
25.
3
8
±
²
³
´
µ
¶
·
1
+ 2
1
=
8
3
+
1
2
=
8
±
2
+
1
±
3
3
±
2
=
16
+
3
6
=
19
6
27.
Commutative (·)
29.
Distributive
31.
Inverse (·)
33.
Inverse (+)
35.
Identity (+)
37.
Negatives (Theorem 1)
39.
The even integers between 3 and 5 are 2, 0, 2, and 4. Hence, the set is
written {2, 0, 2, 4}.
41.
The letters in "status" are:
s,t,a,u
. Hence, the set is written {
s,t,a,u
}, or,
equivalently, {
a,s,t,u
}.
43.
Since there are no months starting with
B
, the set is empty.
±
45.
(A) The empty set,
±
, is a subset of every set.
{
a
} and {
b
} are subsets of
S
2
.
S
2
is a subset of itself.
Thus, there are four subsets of
S
2
.
(B) The empty set,
±
, is a subset of every set.
{
a
}, {
b
}, and {
c
} are onemember subsets of
S
3
.
{
b, c
}, {
a, c
}, and {
a, b
} are twomember subsets of
S
3
.
S
3
is a subset of itself.
Thus, there are 1 + 3 + 3 + 1 = 8 subsets of
S
3
.
(C) The empty set,
±
, is a subset of every set.
{
a
}, {
b
}, {
c
}, and {
d
} are onemember subsets of
S
4
.
{
a, b
}, {
a, c
}, {
a, d
}, {
b, c
}, {
b, d
}, and {
c, d
} are twomember subsets
of
S
4
.
{
b, c, d
}, {
a, c, d
}, {
a, b, d
}, and {
b, c, d
} are threemember subsets
of
S
4
.
S
4
is a subset of itself.
Thus, there are 1 + 4 + 6 + 4 + 1 = 16 subsets of
S
4
.
47.
Yes. This restates Zero Property (2). (Theorem 2, Part 2)
49.
(A) True.
(B) False,
2
3
is an example of a real number that is not irrational.
(C) True.