MATH 190
Fall 2014
Textbook: R. Grimaldi, Discrete and Combinatorial Mathematics: An
Applied Introduction, Pearson. Fifth Edition
Week 4, 5
Chapter 2: Fundamentals of Logic
Dear Students,
In order to understand and improve your skills in the topics covere
Discrete Mathematics for Computing
Fall 2014
Chapter 5: Relations and Functions
= cfw_0, 1, 2, 3, : Set of nonnegative integers
+ = cfw_1, 2, 3, : Set of positive integers
= cfw_ , 3, 2, 1,0, 1, 2, 3, : Set of all integers
= cfw_ | , : Set of all rati
9.
10.
11.
CHAPTER 3
SET THEORY
Section 3.1
They are all the same set.
All of the statements are true except for part (f).
All of the statements are true except for parts (1) and (d).
All of the statements are true except for parts (a) and (b).
(a) cfw_0,
MATH 190
Fall 2014
Textbook: R. Grimaldi, Discrete and Combinatorial Mathematics: An
Applied Introduction, Pearson. Fifth Edition
Weeks 5 & 6
Chapter 3: Set Theory
Dear Students,
In order to better understand and improve your skills in the topics covered
MATH 190
Fall 2014
Textbook: R. Grimaldi, Discrete and Combinatorial Mathematics: An
Applied Introduction, Pearson. Fifth Edition
Weeks 7 & 8
Chapter 4: Properties of the Integers: Mathematical Induction
Dear Students,
In order to better understand and im
Answers
1. Basic Properties of Modular Arithmetic
Exercise 1:
a. = 10
b. = 8
c. = 0
d. = 9
e. = 6
f. = 11
Exercise 2:
a. = 15
b. = 7
c. = 140
Exercise 3: 76, 51, 26, 1, 24, 49, 74, 99.
Exercise 4:
a. No
b. No
c. Yes
d. No
Exercise 5:
a. 13
b. 6
Exercise 6
Discrete Maths for Computing
Practice 6
Answers
Fall 2014
Dr. Rouba Badra
Chapter 1: Counting
1. Basic Principles of Counting
Exercise 1: We use product rule for 4 tasks where each task consists of assigning one of
the 26 English letters: 264 = 456976.
Th
CHAPTER 2
FUNDAMENTALS OF LOGIC
Section 2.1
The sentences in parts (a), (c), (d), and (f) are statements.
The statements in parts (a), (c), and (f) are primitive statements.
Since p -+ q is false the truth value for p is 1 and that of q is 0. Consequently
MATH 190
Fall 2014
R.I.T Dubai
Discrete Mathematics for Computing MATH190
Homework 2 Due Date: Wednesday December 17th 2014
Student Name:
Exercise 1: Let : be a function defined by
+ 5,
() = cfw_ 2 ,
4 1,
0
0<2
2
a) Find 1 (cfw_1), 1 (cfw_6).
b) Find 1 (
Discrete Mathematics for Computing
Fall 2014
Modular Arithmetic
1. Basic Properties of Modular Arithmetic
Exercise 1: Suppose that and are integers, 4 (mod 13), 9 (mod 13). Find the integer
with 0 12 such that
a. 9 (mod 13)
b. 11 (mod 13)
c. + (mod 13)
d
Discrete Mathematics for Computing
Fall 2014
Chapter 1: Counting
1. Basic Principles of Counting
Exercise 1: High school faculties are to be issued special coded identification cards that consist of four
letters of the English alphabet. How many different
Discrete Mathematics for Computing
Fall 2014
Chapter 1: Counting
3. Binomial Coefficients
Exercise 1: Find the expansion of ( + )4
Exercise 2: What is the coefficient of 2 10 in the expansion of ( + )12 ?
Exercise 3: What is the coefficient of 4 6 in the
MATH 190
Fall 2014
Textbook: R. Grimaldi, Discrete and Combinatorial Mathematics: An
Applied Introduction, Pearson. Fifth Edition
Week 2
Chapter 2: Fundamentals of Logic
Dear Students,
In order to understand and improve your skills in the topics covered i
MATH 190
Fall 2014
Textbook: R. Grimaldi, Discrete and Combinatorial Mathematics: An
Applied Introduction, Pearson. Fifth Edition
Week 1
Chapter 2: Fundamentals of Logic
Section 2.1 Basic Connectives and Truth Tables
Dear Students,
In order to understand
1.
Section 2.3
The validity of the argument foilows from the results in the last row. (The rst seven rows
may be ignored.)
The validity of the argument follows from the results in rows 1, 2, and 5 of the table. The
results in the other ve rows may b