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Neal Whittington (whittin3) Tuesdays, at 4:00PM AD9
CS 173: Discrete Structures, Spring 2010
Homework 4
This homework contains 5 problems worth a total of 50 points. It is due on Friday, 19
February at 4pm.
1.
Set Operations [16 points]
Suppose you were given the following sets:
A
=
{
Piano
,
{
Violin
,
Viola
,
Cello
}
,
Guitar
}
B
=
{{
Flute, Piccolo
}
,
Cymbals
}
C
=
{
Piano
,
Flute
}
D
=
{{
Violin, Viola, Cello
}
,
{
Flute, Piccolo
}}
List the elements of the set for the following expressions:
(a)
A
∪
D
{
Piano
,
{
Violin
,
Viola
,
Cello
}
,
Guitar
,
{
Flute, Piccolo
}}
(b)
B
∩
C
∅
(c)
A

(
B

C
)
{
Piano,
{
Violin, Viola, Cello
}}
(d)
A
∩
P
(
B
∩
C
)
∅
(e) (
B
∩
D
)
×
C
{{
Flute, Piccolo
} × {
Piano, Flute
}
=
{{
Flute, Piano
}
,
{
Flute, Flute
}
,
{
Piccolo, Piano
}
,
{
Piccolo, Flute
}}
(f)

P
(
B
∩
D
)

{{
Flute
}
,
{
Piccolo
}
,
{ ∅ }
,
{
Flute, Piccolo
}}
(g)
{
X
∈
P
(
A
) :

X

is not prime
}
(h)
{
X
∈
(
P
(
A
)
∪
P
(
B
)) :

X
 ≡
3
(mod 2)
}
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This note was uploaded on 11/09/2011 for the course CS 173 taught by Professor Erickson during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Erickson

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