CS123
January 19, 2010
Youssef
Homework 1
Due Date: February 2, 2010
Problem 1: (15 points)
let
A
=
{
1
,
3
,
4
,
5
,
7
,
8
,
9
,
11
,
12
}
,
B
=
{
x

x
is an even natural number and 1
< x <
10
}
,
and
C
=
{
a, b, c,
4
,
5
,
6
,
7
,
8
}
.
a)
Fill in the blanks with the most appropriate symbol (
∈
, /
∈
,
⊆
,
6⊆
):
6
...B,
6
...A, b.
..C, b.
..B,
{
2
,
4
,
6
}
...A,
{
2
,
4
,
6
}
...B,
{
4
,
6
,
8
,
10
}
...C.
b)
Evaluate:
A
∪
B, A
∩
B, A

B, A
+
B,
2
A
∩
B
∩
C
,
(
A
∩
B
)
× {
a, b
}
.
c)
Evaluate:
A
∩
(
B
∪
C
)
, A

(
B
∪
C
)
,
(
A

B
)

C,
(
A
+
B
) +
C, A
+ (
B
+
C
).
d)
Find the cardinality of each set in (b) and (c).
Problem 2: (15 points)
Let A be the set of undergraduates at GW, B the set of GW students in discrete math
(CS 12310) at GW in Spring 2010 semester, and C the set of GW students majoring in CS
in Spring 2010. Express each of the following sets in terms of A, B and C (and the diﬀerent
set operations):
a)
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 Spring '09
 Natural number, Prime number, undergraduate CS, GW undergraduate students

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