CSE
105 
HOMEWORK
1
SOLUTIONS
prepared by Lawrence Cayton
0.1
a.
Odd natural numbers
b.
Even integers
c.
Even natural numbers
d.
Even natural numbers that are multiples of 3
e.
Symmetric binary numbers
f.
The empty set
0.2
a.
{
1
,
10
,
100
}
b.
{
x
∈ Z
x >
5
}
c.
{
x
∈ N
x <
5
}
d.
{
aba
}
e.
{
±
}
f.
∅
0.3
a.
No:
A
±⊂
B
b.
Yes:
B
⊂
A
c.
A
∪
B
=
{
x, y, z
}
d.
A
∩
B
=
{
x, y
}
e.
A
×
B
=
{
(
x, x
)
,
(
x, y
)
,
(
y, x
)
,
(
y, y
)
,
(
z, x
)
,
(
z, y
)
}
f.
P
(
B
) =
{∅
,
{
x
}
,
{
y
}
,
{
x, y
}}
0.4
Each element of
A
is paired with each element of
B
, so

A
×
B

=
ab
.
0.5
There are
2
c
elements in the powerset of
C
. Suppose we label each element of
C
with a 1 or 0 and
form the subset of elements of
C
that we labelled with a 1. Then, we can describe each element of the
powerset – any subset of
C
– this way, so the size of the powerset is the number of 01 labellings of
the elements of
C
.
0.6