The Pigeonhole Principle
It is easy to see, and follows immediately from Proposition F2 in the Functions section,
that no function from a set of size at least k + 1 to a set of size k can be 1-1. Thus, some
two elements of the domain have the same image.
Discrete Mathematics (CS 120)
Spring 2013
Test #1 Solutions
Part I: Short-Answer Questions (20 x 2 = 40 points):
1. Given the function above, what are the codomain and domain? domain is A, codomain is B
2. Given the function above, what is the preimage of
Name: _
Student Id: _
Discrete Mathematics (CS 120)
Spring 2013
Test #1 Part I
Part I
Part II
Total
The use of books, notes, electronic devices (including cellphones) as well as communication with others - is not
permitted during the test and may result i
Discrete Mathematics (CS 120)
Fall 2013
Test #2 Solutions
(Solutions appear below in bold font)
Part I: Short-Answer Questions (20 x 2 = 40 points):
1. Other than input and output, name at least four key properties of an algorithm. correct, effective, fin
Name: _
Student Id: _
Discrete Mathematics (CS 120)
Final Examination
December 18, 2013
Part I
Part II
Total
The use of a standard of scientific calculator is permitted. The use of other electronic devices (including cellphones), books and notes
as well
Name: _
Student Id: _
Discrete Mathematics (CS 120)
Test #2 Nov. 13, 2013
Part I
Part II
Total
The use of books, notes, electronic devices (including cellphones) as well as communication with others - is not permitted during the
test and may result in a s
Discrete Mathematics CS 120
Lecture #12
November 20, 2013
Notes by: Haijun Su
Annoucements
Announcement #25
Last night we reviewed Homework #7 - all nine problems worth. Fortunately, all our
arithemtic worked, and one of our students was inspired enough t
Discrete Mathematics CS 120
Lecture #4
October 2, 2013
Notes by: Zhaojiang Ban
Announcements
The first test is October 16th and it will cover the knowledge of Chapter 1 and 2. Each
student should do additional examples and exercises to develop his/her fam
Discrete Mathematics CS 120
Lecture # 8
October 30, 2013
By: Ruibo Chen
Announcements:
Tonights lecture began with a review of the homework assigned from last week,
followed by a brief analysis of the time complexity of insertion sort. We then proceeded
w
Discrete Mathematics (CS 120)
Problem Set #2
Due in class: October 2, 2013
Have your written solutions ready at the beginning of class for review and scoring. (If you cannot
attend class, e-mail your solutions to the instructor at LT.CS320@yahoo.com by 6:
Discrete Mathematics (CS 120)
Problem Set #3
Due in class: October 9, 2013
Have your written solutions ready at the beginning of class for review and scoring. (Only if you
cannot attend class, e-mail your solutions to the instructor at LT.CS320@yahoo.com
ANS
Rosen-2311T MHIA017-Rosen-v5.cls
May 13, 2011
10:29
Answers to Odd-Numbered Exercises
CHAPTER 1
Section 1.1
1. a) Yes, T b) Yes, F c) Yes, T d) Yes, F e) No f) No
3. a) Mei does not have an MP3 player. b) There is pollution
in New Jersey. c) 2 + 1 = 3
STUDY GUIDE FOR THE SECOND EXAM IN DISCRETE MATHEMATICS
General Education.
(1) Why did we study logic in this class?
(2) Why did we study set theory in this class?
(3) Define what it means for a set to be infinite. (Note: this relies on the material we ar
STUDY GUIDE FOR THE FIRST DISCRETE MATH EXAM
1. Combinatorics
Go over combinatorics examples in the text.
Review all the combinatorics problems from homework.
Do at least a couple of extra problems given below.
(1) How many (positive integer) divisors
Discrete Mathematics (CS 120)
Homework #8
Due: December 11, 2013
Have your written solutions ready at the beginning of class for review and scoring. (If you cannot attend
class, e-mail your solutions to the instructor at LT.CS320@yahoo.com by 6:30 p.m. on
Discrete Mathematics (CS 120)
Problem Set #6
Due in class: November 20, 2013
Have your written solutions ready at the beginning of class for review and scoring. (Only if you cannot
attend class, e-mail your solutions to the instructor at LT.CS320@yahoo.co
Discrete Mathematics (CS 120)
Problem Set #6
Due in class: November 6, 2013
Have your written solutions ready at the beginning of class for review and scoring. (Only if you cannot
attend class, e-mail your solutions to the instructor at LT.CS320@yahoo.com
Discrete Mathematics (CS 120)
Problem Set #4
Due in class: October 23, 2013
Have your written solutions ready at the beginning of class for review and scoring. (Only if you cannot
attend class, e-mail your solutions to the instructor at LT.CS320@yahoo.com
Discrete Mathematics (CS 120)
Problem Set #5
Due in class: October 30, 2013
Have your written solutions ready at the beginning of class for review and scoring. (Only if you cannot
attend class, e-mail your solutions to the instructor at LT.CS320@yahoo.com
Discrete Mathematics (CS 120)
Problem Set #1
1. A (binary) set operator % is said to be commutative if A % B = B % A; it is said to be
associative if (A * B) * C = A * (B * C). (Note: % is not any specific operator. It is a
placeholder for an arbitrary op
Discrete Mathematics CS 120
Lecture #11
November 13, 2013
Notes by: Jose Bautista
Announcements
Last night we discussed two topics - (1) Proving the uniquesness of a prime factorization, and (2)
how to use Euclid's Algorithm - backwards - to find the inte
Discrete Mathematics CS 120
Lecture #10
November 6, 2013
Notes by: Andrew Chen
Annoucements
None
Review of Prior Homework
1. A bit-string is a string comprised from binary digits 0 and 1. Give a recursive
definition of a bit-string.
=cfw_0,1
Basis: Bit St