From jacob_otto@hotmail.com Thu Jul 12 21:10:08 2001
Date: Fri, 13 Jul 2001 01:01:57
From: Jacob Otto <jacob_otto@hotmail.com>
To: dimitrik@MIT.EDU
Subject: discrete math, PS-7
Discrete Math Problem
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Problem Set 7 Generating functions, Number Theory, Cryptography
1. Compute by hand, the smallest positive integers x, y, u,
CS123
Spring 2010
Solution to Homework 4
Problem 1 (25 points)
Let (B, +, , , 0, 1) be a Boolean algebra. Dene the following operations and : x y = xy + x y ,
and x y = (x + y ) .
a) Prove that x y =
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Problem Set 6 Combinatorics and Discrete Probability
1. Assume someone is throwing three dice of different colors.
a. How m
ARSDIGITA UNIVERSITY
MONTH 2: DISCRETE MATHEMATICS
PROFESSOR SHAI SIMONSON
PROBLEM SET 5 SOLUTIONS COMBINATORICS AND COUNTING
(1) Given ten points in the plane with no three colinear,
(a) How many die
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Problem Set 5 Combinatorics and Counting
1. Given ten points in the plane with no three collinear,
a. How many different se
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Problem Set 5 Combinatorics and Counting
1. Given ten points in the plane with no three collinear,
a. How many different se
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Problem Set 4 Induction and Recurrence Equations
Thanks to Jerey Radclie and Joe Rizzo for many of the solutions.
Pasted to
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Problem Set 4 Induction and Recurrence Equations
1. Whats wrong with the following proofs by induction?
a. Every binary str
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Problem Set 4 Induction and Recurrence Equations
1. Whats wrong with the following proofs by induction?
a. All binary strin
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Problem Set 7 Generating functions, Number Theory, Cryptography
1. Compute by hand, the smallest positive integers x, y, u,
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Lecture Notes
What is Discrete Math?
Example of continuous math Given a fixed surface area, what are the dimensions of a cy
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Final Examination 100 points
Show all work for partial credit. You may use three hours for this exam. After two
hours, rais
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Final Examination 100 points
Show all work for partial credit. You may use three hours for this exam. After two
hours, rais
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Examination 3 100 points
Show all work for partial credit. You may use two hours for this exam. After one hour,
raise your
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Examination 2 100 points
Show all work for partial credit. You may use two hours for this exam. After one
hour, raise your
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Examination 2 100 points
Show all work for partial credit. You may use two hours for this exam. After one
hour, raise your
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Examination 1 100 points
Show all work for partial credit. You may use two hours for this exam. After one
hour, raise your
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Examination 1 100 points
Show all work for partial credit. You may use two hours for this exam. After one
hour, raise your
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Lecture Notes
What is Discrete Math?
Example of continuous math Given a fixed surface area, what are the dimensions of a cy
ArsDigita University
Month 2: Discrete Mathematics - Professor Shai Simonson
Problem Set 4 Induction and Recurrence Equations
1. Whats wrong with the following proofs by induction?
a. Every binary str
Problem Set 3 Solutions
Jerey M. Radclie
November 16, 2000
Exercise 2
a.
Sloppy Joes solution does not work for a number of reasons. The problem lies in the second
recursive call, in which the bottom
CSci 123 Syllabus
Page 1 of 3
CSci 123.10: Discrete Structures I
Department of Computer Science, The George Washington University
Spring 2010
CRN 41736
Syllabus
Instructor:
Textbook:
Location/Times:
O
CS123
Spring 2010
Solution to Midterm
Problem 1 (25 points)
Let p, q be two propositions. We dene the following operation, denoted
p
a) Show the truth table of
Solution:
p
0
0
1
1
q
0
1
0
1
pq
1
1
1
0
CS123
Spring 2010
Solution to Homework 3
Problem 1 (20 points)
For each of the following 4 relations on the set L of all living people on January 1, 2010, state
(no proof necessary) if the relation is
Problem1
a) f : R R, f ( x ) = 8 x 3 isonetoone.
Proof: x1, x 2 R, 8 x1 3 8 x 2 3 x1 x 2 .
f : R R, f ( x ) = 8 x 3 isonto.
Proof: y R, x R, f ( x ) = y .
y+3
R .
f ( x ) = y 8 x 3 = y x =
8
y + 3
Problem1
a) 6 B , 6 A , b C , b B , cfw_2, 4, 6 A , cfw_2, 4, 6 B , cfw_4, 6, 8,10 C
b)
A B = cfw_1, 2, 3, 4, 5, 6, 7, 8, 9,11,12
A B = cfw_4, 8
A B = cfw_1, 3, 5, 7, 9,11,12
A + B = cfw_1, 2, 3,
CS123
Youssef
March 30, 2010
Homework 4
Due Date: April 20, 2010
Problem 1: (25 points)
Let (B, +, , , 0, 1) be a Boolean algebra. Dene the following operations and
x y = xy + x y , and x y = (x + y )