1. (a) Let
A
=
{
1
,
2
}
and let
B
=
{{
2
}
,
3
}
.
10 marks
i. Find
A
∩
B
∅
ii. Find
A

B
{
1
,
2
}
iii. Find
P
(
B
)
{∅
,
{{
2
}}
,
{
3
}
,
{{
2
}
,
3
}}
iv. True or false?
{∅} ∈ P
(
A
)
False
v. True or false?
{∅} ⊆ P
(
A
)
True
(b) If
A
=
{
a,b,c
}
,
B
=
{
a,c
}
, and
C
=
{
b
}
, give the values of each of the following sets:
i.
A
×
B
{
(
a,a
)
,
(
)
,
(
b,a
)
,
(
b,c
)
,
(
c,a
)
,
(
c,c
)
}
ii.

A
×
B
×
C

6
iii.
A
×
(
B
×
C
)
{
(
a,
(
a,b
))
,
(
a,
(
c, b
))
,
(
b,
(
,
(
b,
(
c,b
,
(
c,
(
))
,
(
c,
(
))
}
iv.
A
×∅
∅
(c) Let
N
be the set of nonempty subsets of some set
S
. Express this de±nition of
N
using
set notation.
N
=
{
X

X
⊆
S
∧
X
±
=
∅}
or
N
=
P
(
S
)
 {∅}
2