Submitted By achintmaxwell

Words 1159

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Words 1159

Pages 5

*

*

Ch. 11 of Discrete and Combinatorial Mathematics

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Exercise 11.1, problems 8, 11 , text-pg:519

Exercise 11.2, problems 1, 6, text-pg:528

Exercise 11.3, problems 5, 20 , text-pg:537

Exercise 11.4, problems 14 , text-pg:553

Exercise 11.5, problems 7 , text-pg:563

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Ch. 12 of Discrete and Combinatorial Mathematics

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Exercise 12.1, problems 11 , text-pg:585

Exercise 12.2, problems 6 , text-pg:604

Exercise 12.3, problems 2 , text-pg:609

Exercise 12.5, problems 3 , text-pg:621

Chapter 11

Exercise 11.1

Problem 8:

Figure 11.10 shows an undirected graph representing a section

of a department store. The vertices indicate where cashiers

are located; the edges denote unblocked aisles between cashiers.

The department store wants to set up a security system where

(plainclothes) guards are placed at certain cashier locations so

that each cashier either has a guard at his or her location or is

only one aisle away from a cashier who has a guard. What is

the smallest number of guards needed?

Figure 11.10

Problem 11:

Let G be a graph that satisfies the condition in Exercise 10.

(a) Must G be loop-free? (b) Could G be a multigraph? (c) If

G has n vertices, can we determine how many edges it has?

Exercise 11.2

Problem 1:

Let G be the undirected graph in Fig. 11.27(a).

a) How many connected subgraphs ofGhave four vertices

and include a cycle?

b) Describe the subgraph G1 (of G) in part (b) of the figure

first, as an induced subgraph and second, in terms of

deleting a vertex of G.

c) Describe the subgraphG2 (ofG) in part (c) of the figure

first, as an induced subgraph and second, in terms of the

deletion of vertices of G.

d) Draw the subgraph of G induced by the set of vertices

U _ {b, c, d, f, i, j}.

e) For the graph G, let the edge e _…...

...Course Design Guide MTH/221 Version 1 1 Course Design Guide College of Information Systems & Technology MTH/221 Version 1 Discrete Math for Information Technology Copyright © 2010 by University of Phoenix. All rights reserved. Course Description Discrete (as opposed to continuous) mathematics is of direct importance to the fields of Computer Science and Information Technology. This branch of mathematics includes studying areas such as set theory, logic, relations, graph theory, and analysis of algorithms. This course is intended to provide students with an understanding of these areas and their use in the field of Information Technology. Policies Faculty and students/learners will be held responsible for understanding and adhering to all policies contained within the following two documents: University policies: You must be logged into the student website to view this document. Instructor policies: This document is posted in the Course Materials forum. University policies are subject to change. Be sure to read the policies at the beginning of each class. Policies may be slightly different depending on the modality in which you attend class. If you have recently changed modalities, read the policies governing your current class modality. Course Materials Grimaldi, R. P. (2004). Discrete and combinatorial mathematics: An applied introduction. (5th ed.). Boston, MA: Pearson Addison Wesley. Article References Albert, I. Thakar, J., Li, S., Zhang, R., & Albert...

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...* MTH/221 Week Four Individual problems: * * Ch. 11 of Discrete and Combinatorial Mathematics * Exercise 11.1, problems 8, 11 , text-pg:519 Exercise 11.2, problems 1, 6, text-pg:528 Exercise 11.3, problems 5, 20 , text-pg:537 Exercise 11.4, problems 14 , text-pg:553 Exercise 11.5, problems 7 , text-pg:563 * Ch. 12 of Discrete and Combinatorial Mathematics * Exercise 12.1, problems 11 , text-pg:585 Exercise 12.2, problems 6 , text-pg:604 Exercise 12.3, problems 2 , text-pg:609 Exercise 12.5, problems 3 , text-pg:621 Chapter 11 Exercise 11.1 Problem 8: Figure 11.10 shows an undirected graph representing a section of a department store. The vertices indicate where cashiers are located; the edges denote unblocked aisles between cashiers. The department store wants to set up a security system where (plainclothes) guards are placed at certain cashier locations so that each cashier either has a guard at his or her location or is only one aisle away from a cashier who has a guard. What is the smallest number of guards needed? Figure 11.10 Problem 11: Let G be a graph that satisfies the condition in Exercise 10. (a) Must G be loop-free? (b) Could G be a multigraph? (c) If G has n vertices, can we determine how many edges it has? Exercise 11.2 Problem 1: Let G be the undirected graph in Fig. 11.27(a). a) How many connected subgraphs ofGhave four vertices and include a cycle? b) Describe...

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... both calculus and computer science can take the class, as well as the students who have taken just one of the two subjects. On the other hand, we are using the exclusive or when we say “Students who have taken calculus or computer science, but not both, can enroll in this class”. Here, we mean that students who have taken both calculus and a computer science course cannot take the class. Only those who have taken exactly one of the two courses can take the class. Similarly, when a menu at a restaurant states, “Soup or salad comes with an entree”, the restaurant almost always means that customers can have either soup or salad, but not both. Hence, this is an exclusive, rather than an inclusive, or. Sometimes, we use or in an exclusive sense. When the exclusive or is used to connect the propositions p and q, the proposition “p or q (but not both)” is obtained. Let p and q be propositions. The exclusive or of p and q, denoted by , is the proposition that is true when exactly one of p and q is true and is false otherwise. Table 4. The truth table for the exclusive or of two propositions | p | Q | | TTFF | TFTF | FTTF | Let p and q be propositions. The implication is the proposition that is false when p is true and q is false and true otherwise. In this implication p is called the hypothesis (or antecedent or premise) and q is called the conclusion (or consequence). Table 5. The truth table for the implication | p | Q | | TTFF | TFTF | TFTT | Because implications...

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...1.1/1.2 1a During a local campaign, eight Republican and five Democratic candidates are nominated for president of the school board. a. If the president is to be one of these candidates, how many possibilities are there for the eventual winner? 8 + 5 = 13 1.4 1a In how many ways can 10 (identical) dimes be distributed among five children if (a) there are no restrictions? The number of combinations of n objects taken r at a time is: C ( n + r – 1 , r ) x1 + x2 + x3 + ... + xn = r x1 + x2 + x3 + x4 + x5 = 10 Translates to: number of dimes given to person 1 + number of dimes given to person 2 + number of dimes given to person 3 + number of dimes given to person 4 + number of dimes given to person 5 10 total dimes n = 5 r = 10 C ( 5 + 10 – 1 , 10 ) C ( 14 , 10 ) 1,001 2.1 2 Identify the primitive statements in problem 1: a. In 2003 George W. Bush was the president of the United States. b. x+3 is a positive integer. c. Fifteen is an even number. d. If Jennifer is late for the party, then her cousin Zachary will be quite angry. e. What time is it? f. As of June 30, 2003, Christine Marie Evert had won the French open a record seven times. 2.2 2 Verify the Absorption Law by means of a truth table. p ∨ (p ∧ q)<->p p or (p and q) p | q | p q | p (p q) | p ∨ (p ∧ q)<->p | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2.3 2b Use truth...

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...MTH 221 Entire Course (Discrete Math For Information) Complete Course http://uopguides.com/downloads/mth-221-entire-course-discrete-math-information-complete-course-2/ Visit Website For More Tutorials : http://uopguides.com Email Us for Any Question or More Final Exams at : Uopguides@gmail.com Individual – Selected Textbook Exercises : Chapter 1 Supplementary Exercises MTH 221 Week 1 DQs (A) Consider the problem of how to arrange a group of n people so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? (B) There is an old joke that goes something like this: “If God is love, love is blind, and Ray Charles is blind, then Ray Charles is God.” Explain, in the terms of first-order logic and predicate calculus, why this reasoning is incorrect. (C) There is an old joke, commonly attributed to Groucho Marx, which goes something like this: “I don’t want to belong to any club that will accept people like me as a member.” Does this statement fall under the purview of Russell’s paradox, or is there an easy semantic way out? Look up the term fuzzy set theory in a search engine of your choice or the University Library, and see if this theory can offer any insights into this statement MTH 221 Week 1 Individual — Selected Textbook Exercises MTH 221 Week 2...

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...MTH 221 (Discrete Math for Information Technology) CompleteClass IF You Want To Purchase A+ Work Then Click The Link Below , Instant Download http://hwnerd.com/Math-221-Discrete-Math-for-Information-Technology-Assignments-1491.htm?categoryId=-1 If You Face Any Problem E- Mail Us At Contact.Hwnerd@Gmail.Com MTH 221 Complete Class Week 1 – 5 All Assignments and Discussion Questions – A+ Graded Course Material Week 1 Individual Assignment Selected Textbook Exercises Complete 12 questions below by choosing at least four from each section. • Ch. 1 of Discrete and Combinatorial Mathematics o Supplementary Exercises 1, 2, 7, 8, 9, 10, 15(a), 18, 24, & 25(a & b) • Ch. 2 of Discrete and Combinatorial Mathematics o Exercise 2.1, problems 2, 3, 10, & 13, o Exercise 2.2, problems 3, 4, & 17 o Exercise 2.3, problems 1 & 4 o Exercise 2.4, problems 1, 2, & 6 o Exercise 2.5, problems 1, 2, & 4 • Ch. 3 of Discrete and Combinatorial Mathematics o Exercise 3.1, problems 1, 2, 18, & 21 o Exercise 3.2, problems 3 & 8 Exercise 3.3, problems 1, 2, 4, & 5 Week 1 DQ 1 Consider the problem of how to arrange a group of npeople so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? Week 1 DQ 2 There is an old joke that goes...

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... + 200 = 216 seats in the last row The last row will have 216 seats. (c) What will be the total number of seats in the theater? From our MATH 203 Live Chat Session #4 on Wednesday evening 26 November 2014 we learned that the Sum of terms in a Sequence has the following formula; Sn = [ n (a1 + an ) ] / 2 So with that said n = 50 for the number of rows in the theater. S50 = [ 50 (a1 + an ) ] / 2 So in this case a1 is the first row which equals 20 seats in that row and an is the last row (50th row) which equals 216 seats in that row from (a) and (b) above.. S50 = [ 50 (20 + 216 ) ] / 2 Sum formula from results above S50 = [ 50 (236 ) ] / 2 20 plus 216 equals 236 S50 = [ 11800 ] / 2 50 times 236 equals 11,800 S50 = 5900 11,800 divided by 2 equals 5,900 The total number of seats in the theater will be 5900 seats....

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...L1.1 Lecture Notes: Logic Justification: Precise and structured reasoning is needed in all sciences including computer science. Logic is the basis of all reasoning. Computer programs are similar to logical proofs. Just as positive whole numbers are the fundamental units for arithmetic, propsitions are the fundamental units of logic. Proposition: A statement that is either true or false. E.g. Today is Monday Today is Tuesday The square root of 4 is 2 The square root of 4 is 1 2 is even, and the square of two is even, and 3 is odd and the square of 3 is odd. The Panthers can clinch a playoff berth with a win, plus a loss by the Rams, a loss or tie by the Saints and Bears, a win by the Seahawks and a tie between the Redskins and Cowboys. (Copied verbatim from the sports page 12/26/2004.) Propositions may be true or false and no preference is given one way or the other. This is sometimes difficult to grasp as we have a “natural” preference for true statements. But “snow is chartreuse” and “snow is white” are both propositions of equal standing though one is true and the other false. Non-propositions: What is today? Is today Monday? Questions are not propositions. You can’t judge whether the question itself is true or false, even though the answer to the question may be true or false. Show me some ID! Similarly, imperative statements lack a truth value. 2x=4 x=y Statements with undetermined variables do not have...

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... when recursion, or at least the principle of recursion, played a role in accomplishing a task, such as a large chore that could be decomposed into smaller chunks that were easier to handle separately, but still had the semblance of the overall task. Did you track the completion of this task in any way to ensure that no pieces were left undone, much like an algorithm keeps placeholders to trace a way back from a recursive trajectory? If so, how did you do it? If not, why did you not? (B) Describe a favorite recreational activity in terms of its iterative components, such as solving a crossword or Sudoku puzzle or playing a game of chess or backgammon. Also, mention any recursive elements that occur. (C) Using a search engine of your choice, look up the term one-way function. This concept arises in cryptography. Explain this concept in your own words, using the terms learned in Ch. 5 regarding functions and their inverses. MTH 221 Week 2 Individual – Selected Textbook Exercises MTH 221 Week 3 DQs MTH 221 Week 3 Individual — Selected Textbook Exercises MTH 221 Week 4 DQs MTH 221 Week 4 Individual – Selected Textbook Exercises MTH 221 Week 5 DQs MTH 221 Week 5 Individual – Selected Textbook Exercises MTH 221 Week 5 Learning Team — Research Presentation MTH 221 Entire Course (Discrete Math For Information) Complete Course Follow Link Below To Get Tutorial https://homeworklance.com/downloads/mth-221-entire-course-discrete-math-information-complete...

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...MTH 221 Entire Course (Discrete Math For Information) Complete Course Follow Link Below To Get Tutorial https://homeworklance.com/downloads/mth-221-entire-course-discrete-math-information-complete-course/ Description: Individual – Selected Textbook Exercises : Chapter 1 Supplementary Exercises MTH 221 Week 1 DQs (A) Consider the problem of how to arrange a group of n people so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? (B) There is an old joke that goes something like this: “If God is love, love is blind, and Ray Charles is blind, then Ray Charles is God.” Explain, in the terms of first-order logic and predicate calculus, why this reasoning is incorrect. (C) There is an old joke, commonly attributed to Groucho Marx, which goes something like this: “I don’t want to belong to any club that will accept people like me as a member.” Does this statement fall under the purview of Russell’s paradox, or is there an easy semantic way out? Look up the term fuzzy set theory in a search engine of your choice or the University Library, and see if this theory can offer any insights into this statement MTH 221 Week 1 Individual — Selected Textbook Exercises MTH 221 Week 2 DQs (A) Describe a situation in your professional or personal life...

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...MTH 221 (Discrete Math for Information Technology) Entire Class IF You Want To Purchase A+ Work Then Click The Link Below , Instant Download http://acehomework.com/MTH-221-Discrete-Math-for-Information-Technology-Entire-Class-66567.htm?categoryId=-1 If You Face Any Problem E- Mail Us At JohnMate1122@gmail.com MTH 221 Complete Class Week 1 – 5 All Assignments and Discussion Questions – A+ Graded Course Material Week 1 Individual Assignment Selected Textbook Exercises Complete 12 questions below by choosing at least four from each section. • Ch. 1 of Discrete and Combinatorial Mathematics o Supplementary Exercises 1, 2, 7, 8, 9, 10, 15(a), 18, 24, & 25(a & b) • Ch. 2 of Discrete and Combinatorial Mathematics o Exercise 2.1, problems 2, 3, 10, & 13, o Exercise 2.2, problems 3, 4, & 17 o Exercise 2.3, problems 1 & 4 o Exercise 2.4, problems 1, 2, & 6 o Exercise 2.5, problems 1, 2, & 4 • Ch. 3 of Discrete and Combinatorial Mathematics o Exercise 3.1, problems 1, 2, 18, & 21 o Exercise 3.2, problems 3 & 8 Exercise 3.3, problems 1, 2, 4, & 5 Week 1 DQ 1 Consider the problem of how to arrange a group of npeople so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? Week 1 DQ 2 There is an old joke that...

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...MTH 221 (Discrete Math for Information Technology) CompleteClass IF You Want To Purchase A+ Work Then Click The Link Below , Instant Download http://hwnerd.com/Math-221-Discrete-Math-for-Information-Technology-Assignments-1491.htm?categoryId=-1 If You Face Any Problem E- Mail Us At Contact.Hwnerd@Gmail.Com MTH 221 Complete Class Week 1 – 5 All Assignments and Discussion Questions – A+ Graded Course Material Week 1 Individual Assignment Selected Textbook Exercises Complete 12 questions below by choosing at least four from each section. • Ch. 1 of Discrete and Combinatorial Mathematics o Supplementary Exercises 1, 2, 7, 8, 9, 10, 15(a), 18, 24, & 25(a & b) • Ch. 2 of Discrete and Combinatorial Mathematics o Exercise 2.1, problems 2, 3, 10, & 13, o Exercise 2.2, problems 3, 4, & 17 o Exercise 2.3, problems 1 & 4 o Exercise 2.4, problems 1, 2, & 6 o Exercise 2.5, problems 1, 2, & 4 • Ch. 3 of Discrete and Combinatorial Mathematics o Exercise 3.1, problems 1, 2, 18, & 21 o Exercise 3.2, problems 3 & 8 Exercise 3.3, problems 1, 2, 4, & 5 Week 1 DQ 1 Consider the problem of how to arrange a group of npeople so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? Week 1 DQ 2 There is an old joke that goes...

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...MTH 221 (Discrete Math for Information Technology) CompleteClass IF You Want To Purchase A+ Work Then Click The Link Below , Instant Download http://hwnerd.com/Math-221-Discrete-Math-for-Information-Technology-Assignments-1491.htm?categoryId=-1 If You Face Any Problem E- Mail Us At Contact.Hwnerd@Gmail.Com MTH 221 Complete Class Week 1 – 5 All Assignments and Discussion Questions – A+ Graded Course Material Week 1 Individual Assignment Selected Textbook Exercises Complete 12 questions below by choosing at least four from each section. • Ch. 1 of Discrete and Combinatorial Mathematics o Supplementary Exercises 1, 2, 7, 8, 9, 10, 15(a), 18, 24, & 25(a & b) • Ch. 2 of Discrete and Combinatorial Mathematics o Exercise 2.1, problems 2, 3, 10, & 13, o Exercise 2.2, problems 3, 4, & 17 o Exercise 2.3, problems 1 & 4 o Exercise 2.4, problems 1, 2, & 6 o Exercise 2.5, problems 1, 2, & 4 • Ch. 3 of Discrete and Combinatorial Mathematics o Exercise 3.1, problems 1, 2, 18, & 21 o Exercise 3.2, problems 3 & 8 Exercise 3.3, problems 1, 2, 4, & 5 Week 1 DQ 1 Consider the problem of how to arrange a group of npeople so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? Week 1 DQ 2 There is an old joke that goes...

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...MTH 221 Entire Course (Discrete Math For Information) Complete Course Follow Link Below To Get Tutorial https://homeworklance.com/downloads/mth-221-entire-course-discrete-math-information-complete-course/ Description: Individual – Selected Textbook Exercises : Chapter 1 Supplementary Exercises MTH 221 Week 1 DQs (A) Consider the problem of how to arrange a group of n people so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? (B) There is an old joke that goes something like this: “If God is love, love is blind, and Ray Charles is blind, then Ray Charles is God.” Explain, in the terms of first-order logic and predicate calculus, why this reasoning is incorrect. (C) There is an old joke, commonly attributed to Groucho Marx, which goes something like this: “I don’t want to belong to any club that will accept people like me as a member.” Does this statement fall under the purview of Russell’s paradox, or is there an easy semantic way out? Look up the term fuzzy set theory in a search engine of your choice or the University Library, and see if this theory can offer any insights into this statement MTH 221 Week 1 Individual — Selected Textbook Exercises MTH 221 Week 2 DQs (A) Describe a situation in your professional or personal life...

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...MTH 221 Entire Course (Discrete Math For Information) Complete Course Follow Link Below To Get Tutorial https://homeworklance.com/downloads/mth-221-entire-course-discrete-math-information-complete-course/ Description: Individual – Selected Textbook Exercises : Chapter 1 Supplementary Exercises MTH 221 Week 1 DQs (A) Consider the problem of how to arrange a group of n people so each person can shake hands with every other person. How might you organize this process? How many times will each person shake hands with someone else? How many handshakes will occur? How must your method vary according to whether or not n is even or odd? (B) There is an old joke that goes something like this: “If God is love, love is blind, and Ray Charles is blind, then Ray Charles is God.” Explain, in the terms of first-order logic and predicate calculus, why this reasoning is incorrect. (C) There is an old joke, commonly attributed to Groucho Marx, which goes something like this: “I don’t want to belong to any club that will accept people like me as a member.” Does this statement fall under the purview of Russell’s paradox, or is there an easy semantic way out? Look up the term fuzzy set theory in a search engine of your choice or the University Library, and see if this theory can offer any insights into this statement MTH 221 Week 1 Individual — Selected Textbook Exercises MTH 221 Week 2 DQs (A) Describe a situation in your professional or personal life...

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