Discrete Structures
CS2800
Prelim 2 Solutions
1. (3 points) How many solutions (x1 , x2 , x3 , x4 ) are there to the equation x1 + x2 + x3 + x4 = 35, where
x1 , x2 , x3 , x4 are natural numbers? (Just write down the combinatorial expression that describes

Discrete Structures
CS2800
Homework 11
Automata
1. Produce a regular expression having the same language as the following automaton:
q1
start
0
q2
0
1
1
q4
q6
1
1
q3
0
1
q5
0
2. Rosen 13.4.12. You may produce an -NFA if you wish.
3. Rosen 13.4.24
4. Given

Discrete Structures
CS2800
Prelim 1
Instructions: This is a 90 minute exam. Please answer the following questions in the provided booklet.
Ensure that your name and netid are on your exam booklet. You may answer the questions in any order, but
please clea

Discrete Structures
CS2800
Homework 3 Solutions
Induction and number theory
1. Rosen 5.2, 4:
(a) P (18) says that you can form 18 cents of postage using 4- and 7-cent stamps. This is true: use two
7-cent stamps and a 4-cent stamp. Similarly P (19) is true

Graphs and Trees
Graphs and trees come up everywhere.
I
We can view the internet as a graph (in many ways)
I
I
I
I
Who points to whom
Niche graphs (Ecology):
I
I
I
who is connected to whom
Web search views web pages as a graph
The vertices are species
Two

Discrete Structures
CS2800
Homework 7
Combinatorics + Probability
For all these questions, explain how you got the answer that you got.
1. Rosen Section 6.2: 6, 10, 16 [Clearly explain what the pigeons and holes are in these three problems.]
2. Rosen Sect

Discrete Structures
CS2800
Homework 8
Probability
For all these questions, explain how you got the answer that you got.
1. Rosen Section 7.3: 4, 6, 16
2. Rosen Section 7.4: 6, 8, 12, 16, 24, 28
1