CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment Solution #6
Due Date: Sunday, Oct 19
Suggested Reading: Rosen Section 5.2 - 5.3; Lehman et al. Chapter 5
These are the problems that you need to turn in. For more practice, you are
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #3
Due Date: Sunday, Sept 21
Suggested Reading: Rosen Sections 1.4 - 1.6; Lehman et al. Chapter 3
These are the problems that you need to turn in. For more practice, you are encoura
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #6
Due Date: Sunday, Oct 19
Suggested Reading: Rosen Section 5.2 - 5.3; Lehman et al. Chapter 5
These are the problems that you need to turn in. For more practice, you are encourage
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #8
Due Date: Sunday, Nov 2
Suggested Reading: Rosen 9.1 and 9.5, LLM 9.4
These are the problems that you need to turn in. For more practice, you are encouraged to
work on the other
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #4
Due Date: Tuesday, Sept 30
Suggested Reading: Rosen Sections 2.2 - 2.3; Lehman et al. Chapter 4.1, 4.3, 4.4
These are the problems that you need to turn in. For more practice, yo
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #2
Due Date: Friday, Sept 12
Suggested Reading: Rosen Sections 1.4 - 1.6; Lehman et al. Chapter 3
These are the problems that you need to turn in. For more practice, you are encoura
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #3
Due Date: Sunday, September 21
Suggested Reading: Rosen Sections 1.7 - 1.8, 2.1; Lehman et al. Chapter 1 and 4.1
These are the problems that you need to turn in. For more practic
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #1
Due Date: Friday, September 5
Suggested Reading: Rosen Sections 1.1 - 1.3; Lehman et al. Sections 1.1, 3.1 - 3.4
These are the problems that you need to hand in for grading. For
Kais/1"
QUIZ l - ComS330 Fall 2016
Duration: 20 minutes Your Name
Your Student Number
[01] Fill out your YES or NO answers in the table:
_ Symon-Wm e
(I) F cfw_02] The empty set is a subset of itself.
F [03] A set can be both an element and a subset of a
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #7
Due Date: Sunday, Oct 26
Suggested Reading: Rosen Section 5.3; LLM Chapter 6.1 - 6.3
These are the problems that you need to turn in. For more practice, you are encouraged to
wor
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #9
Due Date: Tuesday, Nov 11
Suggested Reading: Rosen Section 2.5; LLM Chapter 7.1
These are the problems that you need to turn in. For more practice, you are encouraged to
work on
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #2
Due Date: Friday, Sept 12
Suggested Reading: Rosen Sections 1.4 - 1.6; Lehman et al. Chapter 3
These are the problems that you need to turn in. For more practice, you are encoura
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #5
Due Date: Sunday, Oct 12
Suggested Reading: Rosen Section 5.1 - 5.2; Lehman et al. Chapter 5.1 - 5.3
These are the problems that you need to turn in. For more practice, you are e
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #4
Due Date: Tuesday, Sept 30
Suggested Reading: Rosen Sections 2.2 - 2.3; Lehman et al. Chapter 4.1, 4.3, 4.4
These are the problems that you need to turn in. For more practice, yo
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment #1 Solutions
Due Date: Friday, September 5
Suggested Reading: Rosen Sections 1.1 - 1.3; Lehman et al. Sections 1.1, 3.1 - 3.4
These are the problems that you need to hand in for gra
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment Solutions#5
Due Date: Sunday, Oct 12
Suggested Reading: Rosen Section 5.1 - 5.2; Lehman et al. Chapter 5.1 - 5.3
These are the problems that you need to turn in. For more practice,
CS 330 : Discrete Computational Structures
Fall Semester, 2014
Assignment Solutions #7
Due Date: Sunday, Oct 26
Suggested Reading: Rosen Section 5.3; LLM Chapter 6.1 - 6.3
These are the problems that you need to turn in. For more practice, you are encoura
CS 330 : Discrete Mathematics
Spring Semester, 2016
Assignment #1
Due Date: Friday, January 24
1. EXC 1:
a) B and E , C and D , C and E, E and F
e) X = cfw_1, 2 , Y = cfw_3, 4, cfw_1, 5
2. EXC 2:
a) A B A B
x (A B) x A x B x A x A x B x A B A B A B
b) A (
Solution - ComS 330 - Hw 5
Ghazaleh Parvini
April 2016
33
(a)An example from arithmetic of proving a biconditional via its two parts. Show that for
any positive integers m,n, we have n=m iff each of m,n divides the other.
Suppose n =m. Then n/m = 1, and
1
Chapter 5 - RELATIONS
5.1. RELATIONS AND CARTESIAN PRODUCTS OF SETS
Let B1 , B2 ,., Bn be sets. We have defined the Cartesian product of these sets as follows
B1 B2 . Bn cfw_(a1 , a2 ,., an ) i, ai Bi .
Any subset A B1 B2 . Bn is an n-ary relation on t
HW1 - ComS 330 - SPRING 2016
Due Date - Friday, January 22
GRADING RULE FOR THE SPRING SESSION:
Only about 50-60% of problems in each assignment will be graded!
The choice of problems to be graded will be made after due date.
Solutions to all problems wil
1
Department of Computer Science
Discrete Computational Structures CS 230
Spring 16 , G. Slutzki
Your Name
SO L U T I O N S
Your Student # _
M I D T E R M EXAM I
This is a closed-book, closed-notes, no-calculator, no-crib-sheet exam.
You must use pens, no
HW4 - ComS 330 - SPRING 2016
Due Date - Friday, February 26
GRADING RULE FOR THE SPRING SESSION:
Only about 50-60% of problems in each assignment will be graded!
The choice of problems to be graded will be made after due date.
Solutions to all problems wi
1
Chapter 1 - NAIVE SET THEORY
1.1. SETS & SUBSETS
A set is a collection of objects. The objects are called elements or members of the set. There are
no restrictions on the nature of elements; they can be numbers, programs, houses, people,
DNA sequences,
1
Chapter 3 INDUCTION AND OTHER TRICKS
3.1. GENERALITIES
Statements can be general, like the following three examples
All men are mortal.
Every citizen of United States over the age of 18 is entitled to vote in elections.
Every positive integer whose sum
HW2 - ComS 330 - SPRING 2016
Due Date - Friday, February 12
GRADING RULE FOR THE SPRING SESSION:
Only about 50-60% of problems in each assignment will be graded!
The choice of problems to be graded will be made after due date.
Solutions to all problems wi
HW4 - ComS 330 - SPRING 2016
Due Date - Friday, February 26
GRADING RULE FOR THE SPRING SESSION:
Only about 50-60% of problems in each assignment will be graded!
The choice of problems to be graded will be made after due date.
Solutions to all problems wi
HW1 - ComS 330 - SPRING 2016
Due Date - Friday, January 22?
GRADING RULE FOR THE SPRING SESSION:
Only about 50-60% of problems in each assignment will be graded!
The choice of problems to be graded will be made after due date.
Solutions to all problems wi
HW2 - ComS 330 - SPRING 2016
Due Date - Friday, February 12
GRADING RULE FOR THE SPRING SESSION:
Only about 50-60% of problems in each assignment will be graded!
The choice of problems to be graded will be made after due date.
Solutions to all problems wi
Solution - ComS 330 - Hw 3
Ghazaleh Parvini
February 2016
14:
Suppose f: A B and g : B C are injective. To prove that gof : A C is injective, we need
to prove that if gof (x) = gof (y), then x = y.
Soppose gof (x) = gof (y) = c C.
This means that g(f(x) =
Homework 4
Problems 24 to 31 - solutions
Problem 24. The Pigeonhole Principle: Let A, B be finite sets. If #(A) > k #(B) then for every
function f : A B there is a b B such that b = f (a) for at least k + 1 distinct a A.
In this problem, #(B)=32, the numb
HW5 - ComS 330 - SPRING 2016
Due Date - Friday, March 25
GRADING RULE FOR THE SPRING SESSION:
Only about 50-60% of problems in each assignment will be graded!
The choice of problems to be graded will be made after due date.
Solutions to all problems will
1
Chapter 2 - FUNCTIONS
2.1. FUNCTIONS & COMPOSITION
A function (a.k.a. map, mapping, transformation) consists of three things:
1. A set X, called the domain of the function,
2. A set Y, called the co-domain of the function, and
3. A rule f, assigning to
HW1 - ComS 330 - SPRING 2016
Due Date - Friday, January 29
GRADING RULE FOR THE SPRING SESSION:
Only about 50-60% of problems in each assignment will be graded!
The choice of problems to be graded will be made after due date.
Solutions to all problems wil
Homework 2
Problems 8 and 9 - solutions
Problem 8(a). Let cfw_Ai iI be any collection of sets and let B be any set.
S
(i) iI cfw_Ai B iff Ai B for every i I.
S
Assume that iI cfw_Ai B. We have to prove Ai B for every iS I.
Let x Ai where i is fixed. The