CC 2204
Discrete Mathematics
Tutorial 1
Propositional Logic
Exercise 1.1 Propositional Logic (p. 16)
7. Let p and q be the propositions
p: It is below freezing.
q: It is snowing.
Write these propositions using p and q and logical connectives.
a)
b)
c)
d)

CC 2204
Discrete Mathematics
Tutorial 5
Sequences & Summation & Mathematical Induction
Exercise 2.4 Sequences and Summations (p. 160)
3. What are the terms a0, a1, a2 and a3 of the sequence cfw_an, where an equals
a)
b)
c)
d)
2n + 1 ?
(n + 1)n+1 ?
n / 2

CC 2204
Discrete Mathematics
Tutorial 6
Counting
Exercise 5.1 (p. 344)
1. There are 18 mathematics majors and 325 computer science majors at a college.
a)
How many ways are there to pick two representatives, so that one is a
mathematics major and the othe

CC 2204
Discrete Mathematics
Tutorial 3
Mathematical Proofs
Exercise 1.5 Rules of Inferences (p. 72)
5. Use rules of inference to show that the hypotheses Randy works hard, If Randy
works hard, then he is a dull boy, and If Randy is a dull boy, then he wi

Exercise 2.1 Sets (p. 119)
1. List the members of these sets:
a)
cfw_x | x is a real number such that x2 = 1
b)
cfw_x | x is a positive integer less than 12
c)
cfw_x | x is the square of an integer and x < 100
d)
cfw_x | x is an integer such that x2 = 2
e

CC 2204
Discrete Mathematics
Tutorial 7
Discrete Probability
Exercise 6.1 (p. 398)
5. What is the probability that the sum of the numbers on two dice is even when they are rolled?
9. What is the probability that a five-card poker hand does not contain the

CC 2204
Discrete Mathematics
Tutorial 8
Relations
Exercise 8.1 (p. 527)
3. For each of these relations on the set cfw_1, 2, 3, 4, decide whether it is reflexive,
symmetric, antisymmetric or transitive.
a)
cfw_(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)
b)
cf

College of Professional and Continuing Education (CPCE), an affiliate of PolyU
The Hong Kong Polytechnic University
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
The Hong Kong Polytechnic University
College of Professional

College of Professional and Continuing Education (CPCE), an affiliate of PolyU
The Hong Kong Polytechnic University
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
The Hong Kong Polytechnic University
College of Professional

College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Prof

College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Profess

College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Prof

College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Profess

College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Profess

College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Professional and Continuing Education (CPCE), an affiliate of PolyU
College of Profess

CC 2204
Discrete Mathematics
Tutorial 2
Predicate Logic
Exercise 1.3 Predicates and Quantifiers (p. 46)
5. Let P(x) be the statement x spends more than five hours every weekday in class.
where the universe of discourse for x consists of all students. Expr

CC2204 Discrete Mathematics
Semester 2 2012-2013
Assignment 3 (group work of 4 or 5 students; 20%)
Due: 13 May 2013
Things to do
Answer ALL of the following 50 questions from our textbook,
6th edition, 2007.
Section 8.1 (p. 519): #32, #34, #40, #42
Sectio

CC2204 Discrete Mathematics
Semester 2 2012-2013
Assignment 2 (group work of 4 or 5 students; 20%)
Due: 8 April 2013
Things to do
Answer ALL of the following 50 questions from our textbook, 6 edition,
th
2007.
Section 2.1 Sets (p.119): #2, #8, #22, #28
Se

Lecture8Relations
8.1RelationsandTheirProperties
8.3RepresentingRelations
8.4ClosuresofRelations
03/11/14
1
8.1RelationsandTheirProperties
LetA,Bbeanytwosets.
A(binary)relationRfromAtoB,writtenR:A,B,isa
subsetofAB.
A B = cfw_(a, b) | a A and b B
Thenotat

Lecture 10
Graphs (Part 2)
9.4 Connectivity
9.5 Euler & Hamilton Paths
1
Connectivity
In an undirected graph, a path of length n from u
to v is a sequence of adjacent edges going from
vertex u to vertex v.
A path is a circuit if u = v .
A path pass thr

Lecture4
SetsandFunctions
2.1 Sets
2.2 Set Operations
2.3 Functions
03/11/14
AdoptedfromMichaelP.Frank
1
2.1Sets
A set is a new type of structure, representing an
unordered collection of zero or more distinct
objects.
Set theory deals with operations betw