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Solutions to Homework 2  Math 2000
Notes: Questions 1.21,1.22 were covered in the tutorial. The solution to 1.23 may be
found in the back of the book.
(# 1.17) Let
U
=
{
1
,
3
, . . . ,
15
}
be the universal set,
A
=
{
1
,
5
,
9
,
13
}
, and
B
=
{
3
, ,
9
,
15
}
.
Solution
.
(
a
)
. A
∪
B
=
{
1
,
3
,
5
,
9
,
13
,
15
}
(
b
)
. A
∩
B
=
{
9
}
(
c
)
. A

B
=
{
1
,
5
,
13
}
(
d
)
. B

A
=
{
3
,
15
}
(
e
)
.
A
=
U

A
=
{
3
,
7
,
11
,
15
}
(
f
)
.
B
=
U

B
=
{
1
,
5
,
7
,
11
,
13
}
A
∩
B
=
{
1
,
5
,
13
}
.
(# 1.26) For a real number
r
∈
R
, deﬁne
A
r
=
{
r
2
}
,
B
r
= [
r

1
, r
+ 1], and
C
r
=
(
r,
∞
). Let
S
=
{
1
,
2
,
4
}
. Determine
∪
α
∈
S
A
α
,
∩
α
∈
S
A
α
,
∪
α
∈
S
B
α
,
∩
α
∈
S
B
α
,
∪
α
∈
S
C
α
,
and
∩
α
∈
S
C
α
.
Solution
. (a). We have
[
α
∈
S
A
α
=
A
1
∪
A
2
∪
A
4
=
{
1
2
} ∪ {
2
2
} ∪ {
4
2
}
=
{
1
,
4
,
16
}
.
±
α
∈
S
A
α
=
A
1
∩
A
2
∩
A
4
=
{
1
2
} ∩ {
2
2
} ∩ {
4
2
}
=
φ.
(b). We have
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 Spring '09
 dd
 Math

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