University of Illinois
Fall 2009
ECE 313:
Problem Set 1
Sets, Events, Axioms of Probability and Their Consequences
Due:
Wednesday September 2 at 4 p.m..
Reading:
Ross
Chapter 1, Sections 14; Chapter 2, Sections 15
Powerpoint Lecture Slides, Sets 16
Noncredit Exercises:
Chapter 1:
Problems 15, 7, 9;
Theoretical Exercises 4, 8, 13; SelfTest Problems 115.
Chapter 2:
Problems 3, 4, 9, 10, 1114;
Theoretical Exercises 13, 6, 7, 10, 11, 12, 16, 19, 20; SelfTest Problems 18
Yes, the reading and noncredit exercises are the same as in Problem Set 0.
1.
[Subsets of a finite set]
Let Ω denote a finite set containing the
n
elements
ω
1
, ω
2
, . . . , ω
n
. The
cardinality
(more informally,
the
size
) of a subset
A
⊂
Ω is the number of elements in
A
, and is denoted as

A

.
(a) Let
n
= 4. List
all
the subsets of Ω in increasing order of size. How many subsets are there? How
many of these subsets are
nonempty
subsets?
(b) If you listed only 14 or 15 subsets in part (a), please redo part (a), and this time, include the
empty set
∅
and/or Ω as subsets of Ω.
(c) In your answer to part (a) or (b), verify that for each
k
, 0
≤
k
≤
4, the
total number
of subsets of
size
k
is the same as the
total number
of subsets of size 4

k
. Now explain why for
n
in general,
the total number of subsets of size
k
is the same as the total number of subsets of size
n

k
.
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 Spring '10
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 Empty set, Natural number, University of Illinois

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