Problem Set 5
Section 1.5 (pp 74-75)
#12 For each of these arguments determine whether the argument is correct or incorrect and explain
why:
a) Everyone enrolled in the university has lived in a dormitory. Mia has never lived in a dormitory.
Therefore, Mi

Midterm COMP 2804
February 27, 2014
All questions must be answered on the scantron sheet.
Write your name and student number on the scantron sheet.
You do not have to hand in this examination paper.
This is a closed-book exam.
Calculators are not all

Midterm COMP 2804
October 23, 2013
All questions must be answered on the scantron sheet.
Write your name and student number on the scantron sheet.
You do not have to hand in this examination paper.
Marking scheme: Each of the 17 questions is worth 1 ma

CSI 2101 Discrete Structures
Prof. Lucia Moura
Winter 2010
University of Ottawa
Homework Assignment #2 (100 points, weight 6.25%)
Due: March 8 at 10:00a.m. (in tutorial)
Number Theory
1. (16 points) Exercise 14, page 218 (perfect numbers).
2. (16 points)

CSI 2101 Discrete Structures
Prof. Lucia Moura
Winter 2011
University of Ottawa
Homework Assignment #4 (100 points, weight 6.25%)
Due: Friday, April 8, at 4:00pm (in lecture)
Recurrence relations
1. (30 points) Find the solution to:
an = 5an2 4an4
with a0

COMP 2804 Solutions Assignment 2
Question 1: On the rst page of your assignment, write your name and student number.
Solution:
Name: Sidney Crosby
Student number: 87
Question 2: The function f : N Z is dened by
f (0) = 18,
f (n) = 9(n 2)(n 3) + f (n 1)

CSI 2101 Discrete Structures
Prof. Lucia Moura
Winter 2011
University of Ottawa
Homework Assignment #2 (100 points, weight 6.25%)
Due: Friday, March 18, at 4:00pm (in lecture)
Number Theory
1. (15 points) Show that if a, b, and m are integers such that a

CSI 2101 Discrete Structures
Prof. Lucia Moura
Winter 2010
University of Ottawa
Homework Assignment #1 (100 points, weight 6.25%)
Due: Monday Feb 1, at 10:00 p.m. (in tutorial)
Propositional Logic
1. (12 points) Use logical equivalences to show that [p (p

COMP 2804 Assignment 1
Due: Thursday October 1, before 4:30pm, in the course drop box in Herzberg 3115. Note
that 3115 is open from 8:30am until 4:30pm.
Assignment Policy: Late assignments will not be accepted. Students are encouraged to
collaborate on as

COMP 2804 Assignment 2
Due: Thursday October 15, before 4:30pm, in the course drop box in Herzberg 3115. Note
that 3115 is open from 8:30am until 4:30pm.
Assignment Policy: Late assignments will not be accepted. Students are encouraged to
collaborate on a

CSI 2101 Discrete Structures
Prof. Lucia Moura
Winter 2011
University of Ottawa
Homework Assignment #3 (100 points, weight 6.25%)
Due: Tuesday, March 29, at 2:30pm (in lecture)
Induction
1. For which non-negative integers n is n2 n! ? Prove your answer us

CSI 2101 Discrete Structures
Prof. Lucia Moura
Winter 2010
University of Ottawa
Homework Assignment #4 (100 points (5 bonus), weight 6.25%)
Due: April 9 at 1:00p.m. (in lecture)
Recurrence Relations and Graph Theory
1. (15 marks = 2+2+2+2+2+5) Graphs Theo

CSI 2101 Discrete Structures
Prof. Lucia Moura
Winter 2010
University of Ottawa
Homework Assignment #3 (100 points, weight 6.25%)
Due: March 29 at 10:00a.m. (in tutorial)
Induction and Recursion: Your best 4 questions will be used to calculate your mark.

Midterm COMP 2804
October 24, 2014
All questions must be answered on the scantron sheet.
Write your name and student number on the scantron sheet.
You do not have to hand in this examination paper.
Marking scheme: Each of the 17 questions is worth 1 ma

Midterm COMP 2804
February 24, 2015
All questions must be answered on the scantron sheet.
Write your name and student number on the scantron sheet.
You do not have to hand in this examination paper.
Calculators are allowed.
Marking scheme: Each of the

2
Powers of Integers
An integer n is a perfect square if n = m 2 for some integer m. Taking into account
2
2
the prime factorization, if m = p1 1 pk k , then n = p1 1 pk k . That is, n is a
perfect square if and only if all exponents in its prime factoriz

2
Powers of Integers
An integer n is a perfect square if n = m 2 for some integer m. Taking into account
2
2
the prime factorization, if m = p1 1 pk k , then n = p1 1 pk k . That is, n is a
perfect square if and only if all exponents in its prime factoriz

6.042/18.062J Mathematics for Computer Science
Tom Leighton, Marten van Dijk
September 17, 2010
Notes for Recitation 3
State Machines
1
Recall from Lecture 3 (9/16) that an invariant is a property of a system (in lecture, that
system was the 8-puzzle) tha

SOLUTIONS TO TAKE HOME EXAM 2 MNF130, SPRING 2010
PROBLEM 1
Do one of the following two problems:
(I) Let a1 = 2, a2 = 9 and an = 2an1 + 3an2 for n 3. Show that an 3n for
all positive integers n.
(II) In a round-robin pool tournament there are n participa

Wm
Find more study resources at www.noteso|ution.com
C51 2101
Summary
Winter 2013
Find more study resources at www.motesolution.com Wm Find more study resources at www.motesolution.com
CSI 2101 Summary, Winter 2013
Propositional Logic
- PROPOSITION:

COMP 2804 Solutions Assignment 1
Question 1: On the rst page of your assignment, write your name and student number.
Solution:
Name: James Bond
Student number: 007
Question 2: In Tic-Tac-Toe, we are given a 3 3 grid, consisting of unmarked cells. Two
pl

University of Ottawa
CSI 2101 Midterm Test
Instructor: Lucia Moura
February 9, 2010
11:30 pm
Duration: 1:50 hs
Closed book, no calculators
Last name:
First name:
Student number:
There are 5 questions and 100 marks total.
This exam paper should have 12 pag

CSI 2101 Discrete Structures
Winter 2012
University of Ottawa
Quiz #1
1. S1.3, Exercise 31: Suppose that the domain of Q(x, y, z) consists of triples x, y, z,
where x = 0, 1, or 2, y = 0 or 1, and z = 0 or 1. Write out these propositions using
disjunction

Midterm COMP 2804
February 24, 2015
o All questions must be answered on the soantron sheet.
3 Write your name and student number on the soantron sheet.
3 You do not have to hand in this examination paper.
3 Calculators are allowed.
Marking scheme: Each of

Midterm COMP 2804
October 24, 2014
o All questions must be answered on the soantron sheet.
0 Write your name and student number on the soantron sheet.
0 You do not have to hand in this examination paper.
Marking scheme: Each of the 17 questions is worth 1

CSI2101
DISCRETE STRUCTURES
Winter 2016
WonSook Lee
wslee@uottawa.ca
EECS, Univ. of Ottawa
The lecture note is collaborative work, and
large contribution is from Prof. Nejib Zaguia
4/6/2016
1
Elements of Graph Theory
Quick review on trees and basic conce

CSI2101
DISCRETE STRUCTURES
Winter 2016
WonSook Lee
wslee@uottawa.ca
EECS, Univ. of Ottawa
The lecture note is collaborative work, and
large contribution is from Prof. Nejib Zaguia
4/6/2016
1
Recurrence Relations
Motivation
where do they come from
mode

AVL Trees
Adelson-Velskii and Landis
Data structure that implements MAP ADT
- Height of an AVL Tree
- Insertion and restructuring
- Removal and restructuring
- Costs
CSI2110 (2013) Lucia Moura
1
AVL Tree
AVL trees are
balanced.
An AVL Tree is a binary

CSI2101
DISCRETE STRUCTURES
Winter 2016
WonSook Lee
wslee@uottawa.ca
EECS, Univ. of Ottawa
The lecture note is collaborative work, and
large contribution is from Prof. Nejib Zaguia
1/25/2016
1
Predicate logic (1.4-1.5)
Motivation
Predicates
Quantifiers