Ministry of Higher Education
Kingdom of Saudi Arabia
CSTS
SEU, KSA
Discrete Mathematics (Math-150)
Level III, Assignment-2
(2016-2017)
Section I
State whether the following statements are true or false: (6 marks)
1) A set A has m elements and B has n elem
Ministry of Higher Education
Kingdom of Saudi Arabia
CSTS
SEU, KSA
Discrete Mathematics (Math 150)
Level III, Assignment 1
(2015)
1. State whether the following statements are true or false:
[9]
(a) y (x y) is a tautology.
(a)
(b) The compound proposition
Ministry of Higher Education
Kingdom of Saudi Arabia
CSTS
SEU, KSA
Discrete Mathematics (Math 150)
Level III, Assignment 2
(2015)
1. State whether the following statements are true or false:
[9]
(a) Two sets are equal if and only if they have the same num
Course Name \ MATH-150
Student Name \ HANI ALAHMARI
Academic NO. \ 120002413
CRN NO. \
12177
F2F time \
6-7 PM
Week 5 Practice Exercises
:3.1
Devise an algorithm that finds the sum of all the .3
integers
.in a list
(procedure AddUp(a1, . . . , an: integer
Course Name \ MATH-150
Student Name \ HANI ALAHMARI
Academic NO. \ 120002413
CRN NO. \
12177
F2F time \
6-7 PM
Week 5 Home Work
:3.1
Describe an algorithm that takes as input a list of n integers .6
and finds the number of negative integers in the
.list
F
Course Name \ MATH-150
Student Name \ HANI ALAHMARI
Academic NO. \ 120002413
CRN NO. \
12177
F2F time \
6-7 PM
Week 5 Home work
3.1
Devise an algorithm that finds the sum of all the .3
integers
.in a list
(procedure AddUp(a1, . . . , an: integers .3
sum :
H.W 3
Translate these system specifications into English where .38
the predicate S(x,y)is xis in state y and where the
domain for xand yconsists of all systems and all possible
.states, respectively
(a) xS(x,open
(b) x(S(x,malfunctioning) S(x,diagnostic
(
Week 1 Practice Exercises :1-3
:Section 1-1
Which of these sentences are propositions? What are the truth values of those that are .1
?propositions
(a) Boston is the capital of Massachusetts. . (proposition)(T
(b) Miami is the capital of Florida.
(proposi
Q 1:Determine whether each of these statements is
true or false:
1-the number of function from a set with 3 elements to a set with 6
elements is 18. F
2- the number of different bit strings of length 5 is 32. T
3- P ( n ,0 )=0 . F
C ( n , r )=
4-
n
n!
( n
Saudi Electronic University
College of Computing and Informatics
Assignment of week 7/ Math 150
Section 1: (True or False Questions)
Section 1
1/ 7/3 is a integer.
2
Let a,b,c be integers where a 0 then . if a/b and a/c , then a/(a+b) .
3
In the binary no
1. State whether the following statements are true or false:
(a) x P(x) x P(x)
(a) false
(b) x Q(x) x Q(x)
(b) true
(c) x y Q(x,y) states that for every x there does not exist any y such that Q(x,y).
(c) False
(d) If n is odd integer, then n2 is odd.
(d)
Ministry of Higher Education
Kingdom of Saudi Arabia
CCI, SEU
KSA
Discrete Mathematics (Math 150)
Level III, Assignment 4
(2015)
1. State whether the following statements are true or false:
(a) If a relation is transitive then it is an equivalent relation
Ministry of Higher Education
Kingdom of Saudi Arabia
CCI
SEU, KSA
Discrete Mathematics (Math 150)
Level III, Assignment 2
(2015)
1. State whether the following statements are true or false:
(a) If any two sets are disjoint then their union is the empty se
Saudi Electronic
University College of
Computing and
Informatics Discrete
Mathematics (Math 150)
Assignment week 13
1. Determine whether each of these statements is
true or false.
a
An undirected graph has an even number of vertices of odd degree. (T)
A c
Week2 For Students
Q 1: Determine wheather of the statement true or false:
1- x 2 + y 2 = z 2 is not proposition. F
2-the conditional statement is false when both and are false. F
3-~(~ ) and are logically equivalent. T
4-~ is a contradiction. F
5- the bi
Fares Sajed Sharab * 120009624
Week 8 Homework
o Section 6.1
o
o
o
o
Fares Sajed Sharab * 120009624
Week 8 Homework
o Section 6.2
o
o
o
Fares Sajed Sharab * 120009624
o Week 8 Homework
o Section 6.3
o
o
o
Fares Sajed Sharab * 120009624
o
Fares Sajed Sha
3.2 The Growth of Functions
Definition 1:
Big-Omega and Big-Theta Notation
DEFINITION 2
f (x) is (g(x) if and only if g(x) is O(f (x).
DEFINITION 3
When f (x) is (g(x), it is also the case that g(x) is
(f (x). Also note that f (x) is (g(x) if and only if
MATH 150
Chapter 2
Sets 2.1
DEFINITION 1
A set is an unordered collection of objects,
called elements or members of the set. A set is
said to contain its elements. We write a A
to denote that a is an element of the set A.
The notation a A denotes that a i
MATH150 11
Q1. There are two steps in Mathematical Induction. One is Basis Step and another one is
Secondary Step (2) Inductive step (3) Big Step
Q2. If f(0)=3 and f(n+1)=2f(n)+3 then f(1) is
9 (b)6 (c)4
Q3. A new company with two employees Mohammed and
CHAPTER 6
Counting
6.1 The Basics of Counting
we Well present some of basic counting
priciples:
- the product rule
- the sum rule
- the subtraction rule
- the division rule
THE PRODUCT RULE
Suppose that a procedure can be broken down into a
sequence of tw
1. State whether the following statements are true or false:
(a) If a relation is transitive then it is an equivalent relation. False
(b) The relation R = cfw_(1, 1), (1, 2), (2, 2), (2, 3), (3, 3), (1, 3) is reflexive on the set
A = cfw_1, 2, 3, . True
(
Remarks: read p415 binomial coefficient and identities carefully
(Binomial Theorem) is very important and all section 6.4
Concentrate on:
1- chapter 10 (graphs and representation by matrices).
2-chapter 9 relations
3-chapter 8, how to solve a recurrence r
Question 1 :
1- What are the negations of the following statements:
a- x ( x =4 )
b- x (x >1 x >1)
c- x y (x > y x < y )
2
2
2
Sol:
2
a) x (x 4)
b) Convert to
Now negate:
x ( ( x >1 ) ( x 2> 1 )
2
x ( (x>1) (x >1)
.
x ( x >1)( x 2 1)
c
x y (x2 y x y)
Ministry of Higher Education
Kingdom of Saudi Arabia
CCI
SEU, KSA
Discrete Mathematics (Math 150)
Level III, Assignment
1 (2015)
1. State whether the following statements are true or false:
(a) x + 4 = 7 is a proposition.
(b) The proposition p q is called
Q1
F
T
F
F
F
T
F
F
T
Q2
B
D
C
D
B
D
C
B
B
Q 5.
1 3 4 5 6 8 9 11
First step: is split and dividing this list which has 8 terms into two smaller lists with 4 terms each namely
.1 3 4 5
6 8 9 1 1
.2nd step is: because 5
.6 8
9 11
. 3rd step because 8
.9
9 co
1. State whether the following statements are true or false:
3
(a) If n is a positive integer, then n + 2n is divisible by 3. True
(b) The recursive definition of the set of odd positive integers S is defined as 1 s,
and if n S then n + 1 S.
False
(c) The
Omnyah Abdullah 120007459
Week 9 Practice Exercises
o Section 8.1
o
o
Omnyah Abdullah 120007459
o
Omnyah Abdullah 120007459
Week 9 Practice Exercises
o Section 8.2
o
o
o
Omnyah Abdullah 120007459
o
o
Omnyah Abdullah 120007459
Week 9 Practice Exercises
Ministry of Higher Education
Kingdom of Saudi Arabia
CCI
SEU, KSA
Discrete Mathematics (Math 150)
Level III, Assignment 1
(2015)
1. State whether the following statements are true or false:
(a) x + 4 = 7 is a proposition.
(a)
False
(b)
True
(c)
True
(d)
F
CS 441 Discrete Mathematics for CS
Lecture 23
Relations III.
Milos Hauskrecht
milos@cs.pitt.edu
5329 Sennott Square
M. Hauskrecht
CS 441 Discrete mathematics for CS
Composite of relations
Definition: Let R be a relation from a set A to a set B and S a
rel
Week 9 Study Notes
9.1 Mathematical Induction (Text Section 5.1)
Mathematical induction is a proof technique that can be applied in many situations involving
discrete objects. This technique is particularly useful when we want to prove something is true
f
DISCRETE MATHEMATICS (MATH150)
Level III
ASSIGNMENT-1
2016
Section-I
1.State whether the following statements are True or False.
(9X1=9 Marks)
(a) The conditional statement p q is true if p is false and q is false.
(a)
(b) The contrapositive of p q is q
Qasim A. Al-Obaid
Week 7 Practice Exercises
o Section 5.1
o
120013720
Qasim A. Al-Obaid
o
o
120013720
Qasim A. Al-Obaid
o
120013720
Qasim A. Al-Obaid
o
o
120013720
Qasim A. Al-Obaid
o
o
120013720
Qasim A. Al-Obaid
o
120013720
Qasim A. Al-Obaid
o
1
Qasim A. Al-Obaid
Week 11 Homework
o Section 9.1
o
o
120013720
Qasim A. Al-Obaid
o
o
120013720
Qasim A. Al-Obaid
Week 11 Homework
o Section 9.2
o
o
o
o
120013720
Qasim A. Al-Obaid
o Week 11 Homework
o Section 9.3
o
o
o
120013720
Qasim A. Al-Obaid
o
Qasim A. Al-Obaid
Week 9 Practice Exercises
o Section 8.1
o
o
120013720
Qasim A. Al-Obaid
o
120013720
Qasim A. Al-Obaid
Week 9 Practice Exercises
o Section 8.2
o
o
o
120013720
Qasim A. Al-Obaid
o
o
120013720
Qasim A. Al-Obaid
Week 9 Practice Exerci