due Feb. 1
2.1
6
[E] Determine whether
{
2
}
is an element of the following sets.
a)
{
x
∈
R

x
is an integer greater than 1
}
.
b)
{
x
∈
R

x
is the square of an integer
}
.
c)
{
2
,
{
2
}}
.
d)
{{
2
}
,
{{
2
}}}
.
e)
{{
2
}
,
{
2
,
{
2
}}}
.
f)
{{{
2
}}}
.
8
[E] Determine whether each of these statements is true or false.
a)
∅ ∈ {∅}
.
b)
∅ ∈ {∅
,
{∅}}
.
c)
{∅} ∈ {∅}
.
d)
{∅} ∈ {{∅}}
.
e)
{∅} ⊂ {∅
,
{∅}}
.
f)
{{∅}} ⊂ {∅
,
{∅}}
.
g)
{{∅}} ⊂ {{∅}
,
{∅}}
.
22
[M] Determine whether each of these sets is the power set of a set, where
a
and
b
are distinct elements.
a)
∅
b)
{∅
,
{
a
}}
c)
{∅
,
{
a
}
,
{∅
,a
}}
d)
{∅
,
{
a
}
,
{
b
}
,
{
a,b
}}
28
[M] Let
A
=
{
a,b,c
}
,B
=
{
x,y
}
, and
C
=
{
0
,
1
}
. Find
a)
A
×
B
×
C
b)
C
×
B
×
A
c)
C
×
A
×
B
d)
B
×
B
×
B
2.2
2
[E] Suppose that
A
is the set of sophomores at your school and
B
is the set of
students in discrete mathematics at your school. Express each of these sets in