DeMorgans Laws
( p q ) (p) (q)
(p q ) (p) (q)
p
q
pq
1
1
1
1
0
0
0
(pq)
p
q
(p) (q)
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
(Peter is tall and fat)
Peter is not tall Peter is not fat
(cucumbers are green or seedy)
cucumbers are not green cucumbers are
Outline of COT 3100 material for first exam I. Logic A. Symbols(, and ) B. Truth Tables C. Logic Laws D. Methods of showing equality of logical expressions E. Implication Rules F. Contrapositive of a stmt. G. Quantifiers II. Sets A. Symbols( , , , , , , a
Classification of Combinatorial problems
i) Order matters / does not matter
Choose a committee of 3 out of 10 members
(members are distinguishable): the order of the
members in committee does not matter
10! 10 9 8
C (10, 3) =
=
3!7!
3!
Choose president,
THE FOUNDATIONS:
LOGIC AND PROOFS
Chapter 1
Section 1.4 : Predicates and Quantifiers
Predicates and Quantifiers
Propositional logic, studied in the previous sections, cannot
adequately express the meaning of all statements in
mathematics and in natural la
COT 3100H Spring 2008 Homework #1 Assigned: 1/8/08 Due: 1/15/08
1) Write out a truth table for the following logical expressions: a) [ p ( p q )] q c) p (q (p r ) 2) Determine all truth value assignments for the primitive statements p, q, r, s, t that mak
/ Sean Szumlanski
/ COP 3502, Summer 2016
/ dma_part2.c
/ =
/ Dynamic allocation of 1D arrays.
#include <stdio.h>
#include <stdlib.h>
/ This is a bit tongueincheek. You'll see me use it throughout the semester.
void panic(char *err_msg)
cfw_
fprintf(std
COT 3100
Spring2001
Assignment #1
Solution Key
#1 (p. 13, #18). There are seven different basic systems, four modems, three CD ROM
drives and six different printers. How many different 4 configurations can be made from
these elements?
Ans: 7 4 3 6=504
#2.
COT 3100C Recitation #2 summer 2016
Question 1: Express each of these statements using predicates and
quantifiers.
a) A passenger on an airline qualifies as an elite flyer if the passenger flies more than 25,000
miles in a year or takes more than 25 fligh
Chapter 1.1: Exercise 6: Let p and q be the propositions "The election is decided" and "The votes have been counted", respectively. Express each of these compound propositions as an English sentence. No a b c d e f g h Proposition p p q p q qp q p p q pq
Assignment #2
Due Tuesday, 1/27 Complete the following exercises from chapter 1.3: 2, 8, 10 Complete the following exercises from chapter 1.4: d 14, 28, 32(a,b, and d) Complete the following exercises from chapter 1.5: 14, 24 J For question 14, translate
Due Tuesday, 2/24
Assignment #5
Complete the following exercises from chapter 2.2: h 2, 26, 30 For question 30 in particular, justify your answers Complete the following exercises from chapter 2.3: 6, 8, 12, 16, 22, 28, 32 Honor Section:
Due Tuesday, 2/
Honors Introduction to Discrete Structures COT 3100H Exam #1: Logic, Sets Date: 1/31/08 Solutions 1) (10 pts) Complete the following truth table. Please designate expressions for the intermediate columns in the table. (r p ) p F F F F T T T T q F F T T F
Revised Printing
EEL 3801
Computer
Organization
Fall 2012 (UCF)
Chapter 2
Principles of Machine Design
1.
2.
Instructions are represented as numbers and, as
such, are indistinguishable from data
Programs are stored in alterable memory (that can
be read or
COT 3100
Slides 10/09
Topics
Proof By Induction
Strong Induction
Assigned Reading: Chapter 4.1 4.2
Assignment #3 (Due on 10/18)
For detailed problems, please refer to
Webcourses@UCF.
You should work on 4.1 and 4.2 [Rosen6]
Proof By Induction
We're trying
COT 3100
Slides 08/21
Topics
Syllabus
Logic Fundamentals
Truth tables for compound propositions
Propositional Equivalences
Assigned Reading: Chapter 1.1 1.2
[Rosen6]
Announcements
One copy of each textbooks in library reserve desk [Rosen7] from next
Week.
COT 3100H Spring 2008 Homework #4 Solutions
1) The House currently has 199 Republicans, 232 Democrats and four vacancies. (Nathan corrected my information.) Answer the following questions about forming committees in the House. (a) How many committees can
COT 3100
Slides 08/23
Topics
Truth tables for compound propositions
Propositional Equivalences
Assigned Reading: Chapter 1.1 1.2 [Rosen6],
Announcements:


NO Recitation today.
One copy of the textbook (7th edition) at the library
course reserves. You b
COT 3100
Slides 08/28
Announcements
One copy of the textbook [Rosen 7] in library reserve desk.
It is encouraged that all assignments are typed in Word or Latex.
If you want to handwrite the assignments, it should be easy to
understand.
The order of your
COT 3100
Slides 08/30
Assignment #1 (due 09/13)
You should start working on problems for 1.4
and 1.4 after this lecture (Based on 6th Edition,
For 7th Edition and UCF7slim Edition, check
your webcourses@UCF.)
 Complete the following exercises from
chapte
/Discreet Programming assignment 1
/Programmed in C+ for educational purposes
/ the only c+  specific syntax used is the i/o.
/
By David Callies
/
/
1/9/08
#include<iostream>
u
using namespace std;
#define
#define
#define
#
#define
BIT_A
BIT_B
BIT_C
BIT_
COT 3100 Final Exam 12/5/06 Name: _ Lecturer: Arup Guha TA: _ Section: _
(Note: You will have 2 hours and 50 minutes for this exam. Make sure to read AND follow all the directions. If you need extra room for your work, put it on the last page of the exam
Spring 2008 COT 3100 Homework #5 Grading Criteria  100 points 1) 15 points 5 pts for stay, 10 pts for switch ( 3 pts for 4/5, 3 pts for multiply, 4 pts for 1/3) 2) 10 points 4 points for numerator, 3 pts for second term in denominator, 1pt for adding the
/*
* Name: Amy Hoover
* Assignment: Homework 1
* Class: COT 3100H
* Date: 1/15/08
*/
import java.util.*;
p
public class Homework1 cfw_
byte op1 = 0;
byte op2 = 0;
b
byte op3 = 0;
/Homework object stores the three operators set by the user
public Homework1
COT 3100H Spring 2008 Homework #2 Assigned: 1/15/08 Due: 1/22/08
1) Prove that the fourth power of an odd integer leaves a remainder of 1 when divided by 16. (Hint: You may want to first prove that the expression a(a+1) or a(3a+1) is even for all integers
COT 3100H Spring 2008 Homework #7 Assigned: 3/4/08 (Tuesday) Due: 3/6/08 (Thursday)
1) Find GCD(729, 321) using Euclid's Algorithm. 2) Find all integer solutions for x and y to the equation 729x + 321y = gcd(729, 321). 3) Find all integer solutions for x
Spring 2008 COT 3100 Homework #3 Grading Criteria  100 points 1) a) 10 pts 6 pts to prove subset, 4 pts to prove proper b) 10 pts 5 pts to say false, 5 pts for the counter example 2) a) 10 pts 4 pts for first step, 3 pts for steps 2 and 3 b) 15 pts 3 pts
/Scott Dyl
/COT3100H
/
/Homework #2
import java.util.Scanner;
import java.util.TreeSet;
i
import java.util.Vector;
p
public class Hw2 cfw_
p
public static void main(String[] args) cfw_
TreeSet<Integer> setA = new TreeSet<Integer>();
T
TreeSet<Integer> set
H. CL r premise,
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:23 Universoul Gene/mtkwiaJr'xo
Prove for a inJrCaSn) n(n+l) .s wen.
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The Growth of Func/ons and Algorithm
Complexity
COT3100 Introduc/on to Discrete Structures
Dr. Demetrios Glinos
Readings
Discrete Mathema/cs and its Applica/ons, 7th Edi/on, by Kenneth H. Rosen
(ISBN: 0073383090, UCF Custom Version ISBN:
Proposi'onal Equivalences and Applica'ons
COT3100 Introduc'on to Discrete Structures
Dr. Demetrios Glinos
Readings
Discrete Mathema'cs and its Applica'ons, 7th Edi'on, by Kenneth H. Rosen
(ISBN: 0073383090, UCF Custom Version ISBN: 00777