Concordia University
Department of Computer Science & Software Engineering
COMP 232/2
Mathematics for Computer Science
Fall 2016
Assignment 1 Due date: September 29, 2016
1. For each of the following statements use a truth table to determine whether it is
COMP232 - Mathematics for Computer Science
Tutorial 2
Ali Moallemi
moa ali@encs.concordia.ca
Concordia University, Fall 2016
Ali Moallemi, Iraj Hedayati
COMP232 - Mathematics for Computer Science
1/7
Table of Contents
1
1.2 Applications of Propositional L
Concordia University
Department of Computer Science & Software Engineering
Mathematics for Computer Science
COMP 232/4
Winter 2016
Assignment 1 Solutions
1. For each of the following statements use a truth table to determine whether it is a tautology,
a c
Concordia University
Department of Computer Science & Software Engineering
COMP 232/4
Mathematics for Computer Science
Winter 2016
Assignment 1 Due date: January 29, 2016
1. For each of the following statements use a truth table to determine whether it is
Propositional functions of two variables
Example:
Let R(x, y) be the predicate x2 x + y.
R(1, 0) 12 1 + 0 True
R(5, 2) 52 5 + 2 True
R(0, 2) 02 0 + 2 False
We need multiple quantifiers to turn a propositional function of many variables into a proposition.
Discrete Mathematics
Discrete mathematics is devoted to the study
of discrete or distinct unconnected objects.
Classical mathematics deals with functions
on real numbers. Real numbers form a
continuous line. Some calculus techniques
apply only to contin
Predicates and Quantifiers
Statements involving variables, like
x2 x + 2
The American city is polluted.
are not propositions, since their truth values
depend on the values of the variable involved.
For what value of x?
Which city?
1
Nevertheless, we somet
COMP232 - Mathematics for Computer Science
Tutorial 2
Ali Moallemi
moa ali@encs.concordia.ca
Iraj Hedayati
h iraj@encs.concordia.ca
Concordia University, Fall 2016
Ali Moallemi & Iraj Hedayati
COMP232 - Mathematics for Computer Science
1 / 15
Table of Con
Proofs in Logic
Valid and Invalid Arguments
An argument is a sequence of statements.
Example:
p
q
r
s
Here p, q, and r are called premises and s is
called the conclusion.
An argument is called valid if the truth of the
conclusion follows necessarily (by