Solutions to Homework 3  Math 2000
Notes: Check the back of the book for solutions to 2.1,2.5,2.9. 2.11 was done during
tutorial.
(# 2.2) Consider the sets
A,B,C
, and
D
deﬁned below. Which of the following state
ments are true? Give an explanation for each false statement.
A
=
{
1
,
4
,
7
,
10
,
13
,
16
,...
}
B
=
{
x
∈
Z

x
is odd
}
C
=
{
x
∈
Z

x
is prime and
x
6
= 2
}
D
=
{
1
,
2
,
3
,
5
,
8
,
13
,
21
,
34
,
55
,...
}
.
Solution
. (a). Note that
A
may also be written as
A
=
{
n
∈
N

n
= 3
x
+ 1 with
x
∈
Z
}
.
However, 25 = 3
·
8 + 1 and thus 25
∈
A
. Therefore 25
∈
A
is true.
(b). Since 33 is odd, it follows that 33
∈
D
is true.
(c). 22
/
∈
A
∪
D
is false. Note that 22 = 3
·
7+1 and thus 22
∈
A
and hence 22
∈
A
∪
D
too.
(d).
C
⊆
B
is false since 7
∈
C
but 7
/
∈
B
.
(e).
φ
∈
B
∩
D
is false since
φ
is a subset but not an element of
B
∩
D
.
(f) 53
/
∈
C
is false since 53 is a prime number. (It suﬃces to check whether 53 is
divisible by any primes
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 Spring '09
 dd
 Sets, following statements, Prime number

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