CITY UNIVERSITY OF HONG KONG
Course code & title : MA2504 Discrete Mathematics
Session : Semester B 1999-2000
Time allowed : Three hours
This paper has THREE pages.
1. This paper consists of 4 questions.
2. Answer ALL questions. Question 1. [25 marks] L
ma2185a1
Logic
1. If p stands for it rains in Paris and q stands for we bring umbrellas, then express each of the
following in symbolic form.
(a) If it rains in Paris, then we bring our umbrellas.
(b) It does not rain in Paris and we bring umbrellas.
(c)
MATHEMATICAL LOGIC
1
Introduction
2
Propositions and logical operators
3
Algebra of propositions
4
Predicates and quantifiers
5
Logical inference
1
INTRODUCTION
With the advance of computer technology, computers are essential in many engineering products.
City University of Hong Kong
MA2185 Discrete Mathematics
Instructor: Dr. Andrea CAPONNETTO,
Office: Y6542, Phone: 3442-6466,
E-mail: [email protected]
Assistant: ZHONG Jie,
E-mail: [email protected]
Lecture:
LT-5 Wed 16:00 18:50
16:00-16:50
Discrete Mathematics
MA2185 MA2144
Lecture 07/24
Wednesday, September 24, 2014
Logic, like whiskey, loses its benecial eect when
taken in too large quantities.
Lord Dunsany
Methods of proving theorems
1
Proof of the contrapositive:
A B B A.
In order to p
Discrete Mathematics
MA2185 MA2144
Lecture 03/24
Wednesday, September 10, 2014
Logic is the beginning of all wisdom, not the end.
Spock
What we have encountered thus far
Propositions
Propositional forms
Connectives (, , , , )
truth tables
logical equival
Discrete Mathematics
MA2185 MA2144
Lecture 05/24
Wednesday, September 17, 2014
For the things we have to learn before we can do
them, we learn by doing them.
Aristotle
Predicate calculus what was that again?
predicate: statement, which may depend on vari
Discrete Mathematics
MA2185 MA2144
Lecture 02/24
Thursday, September 04, 2014
Reminder
next Tuesday, 9 September:
Mid-Autumn Festival
no tutorials on this public holiday
every student shall go to a tutorial on
Monday, 8 September
times & rooms:
1
2
3
14:0
ma2185a2
Sets, Relations and Functions
1. For each of the following, choose an appropriate universe of discourse and a predicate to define the set
and its complement.
(a) The set of all odd integers
(b) The set of human fathers
(c) The set of tautologies
ma2185a1
Logic
1. If p stands for it rains in Paris and q stands for we bring umbrellas, then express each of the
following in symbolic form
(a) if it rains in Paris, then we bring our umbrellas,
(b) it does not rain in Paris and we bring umbrellas,
(c) i
CITY UNIVERSITY OF HONG KONG
_—_—_—_————————
Course code and title : MA2184 Discrete Mathematics for Computing
Session : Semester B, 2007-2008
Time allowed : Two Hours
_———_——-——————
This paper has FIVE pages (including this page).
—_—_——_——————————
lnstr
CITY UNIVERSITY OF HONG KONG
Course code and title : MA2184 Discrete Mathematics for Computing
Session : Semester B, 2008-2009
Time allowed : Two Hours
This paper has THREE pages (including this page).
Instructions to candidates:
1. This paper has FIVE qu
CITY UNIVERSITY OF HONG KONG
MM
Module code & title : MA0144 Discrete Mathematics
Session : Semester A, 1996-97
Time Allowed : Two hours
This paper has Three pages. (including this page)
Instructions to candidates:
1. Answer ALL questions.
2. Each que
CITY UNIVERSITY OF HONG KONG
Module code & title : MA1101 Discrete Mathematics I
Session : Semester A, 1996-97
Time Allowed : Three hours
This paper has THREE pages. (including this page)
Instructions to candidates:
1. Attempt all ALL questions.
2.
CITY UNIVERSITY OF HONG KONG
Course code and title : MA2184 Discrete Mathematics for Computing
Session : Semester B, 2005-2006
Time allowed : Two Hours
This paper has THREE pages (including this page).
Instructions to candidates:
1. This paper has Five qu
MA2185 Discrete Mathematics
Part I
Course Duration: One semester
Credit Units: 3
Level: B2
Medium of Instruction: English
Prerequisites: Nil
Precursors: Nil
Equivalent Courses: Nil
Exclusive Courses: MA2144, MA2184, MA2504
Part II
Course Aims
This course
SETS, RELATIONS AND FUNCTIONS
1
2
3
4
Introduction
Basic set theory
Relations
Functions
1
INTRODUCTION
The concept of sets is of fundamental importance in mathematics. We are interested in sets because of their
usefulness in modelling and investigating pr
ma2185a3
Combinatorics
1. Using pigeon hole principal show that in any gathering of six people there are either three people who all
know each other or three people none of whom knows either of the other two.
2.
(a) If A and B are finite sets with number
Discrete Mathematics
MA2185 MA2144
Lecture 01/24
Wednesday, September 03, 2014
Before we start. . .
Some organizational matters:
blackboard. There you will nd
the script (as we go along)
the slides (put there after each lecture)
the assignments (usually o
Discrete Mathematics
MA2185 MA2144
Lecture 04/24
Thursday, September 11, 2014
Predicates and Quantiers
Consider the following statement:
x is an integer
2
Its truth depends on the value of x.
If x is an even integer, then the statement is true.
If x is a
Discrete Mathematics
MA2185 MA2144
Lecture 17/24
Wednesday, November 5, 2014
Combinatorics what we have seen so far
(L Chapter 6 in Rosens book)
Two dierent kind of subjects:
1
Counting techniques
Product Rule
Sum Rule
Urn Models
2
Existence results
Pigeo
Discrete Mathematics
MA2185 MA2144
Lecture 14/24
Thursday, October 23, 2014
Recap: Mid-term test
(1a) Simplify the following expression as much as possible:
(p q) (p q)
(Version B: exchange p and q)
Solution: Using p q p q, we obtain
(p q) (p q)
(p q) (p
Discrete Mathematics
MA2185 MA2144
Lecture 11/24
Wednesday, October 15, 2014
Reference to course material
For further readings on the relations and functions, see
L Sections 9.1 9.3, 9.5 and 2.3 in
Discrete Mathematics and Its Applications by Kenneth H. R
Discrete Mathematics
MA2185 MA2144
Lecture 09/24
Wednesday, October 8, 2014
Overview
1
Mathematical Logic
2
Sets, Relations, Functions
3
Combinatorics
Reference to course material
For further readings on the basics of set theory, see
L Sections 2.1 & 2.2