Discrete math knights and knaves books

So what a says is false, and so there are zero knaves. Knight and knaves logic problem mathematics stack exchange. In these puzzles, we imagine that there is an island that is home to precisely two kinds of people. There are questions posed in the text and problems at the end of each chapter with solutions. You might remember a knights and knaves puzzle from the 1986 fantasy film, labyrinth. On the island of knights and knaves you encounter two people, a and b. The goal of the puzzle is to determine which statements are true based on the information given.

Another feature that is not covered in other discrete mathematics books is the use of estimates. You are on an island where there are living only two types of people. B tells you of a and myself, at least one of us is a knight. From discrete mathematics and its applications, a book by kenneth h. Each is either a knight, who always tells the truth, or a knave, who always lies. An islander call him a made a statement about himself and a. Johns statement cannot be true, because a knave admitting to being a knave would be the same as a liar telling the lie i am a liar, which is known as the liar paradox. Suppose are three people in the island of knights and knaves the knights are people who speak only the truth and knaves are the people who always lie. Free discrete mathematics books download ebooks online. Relate to inhabitants of the island of knights and.

Buy discrete mathematics with application 4th edition 97804953926 by susanna s. Knights and knaves logic circuits propositional logic can be applied to the design of computer hardware. Knights and knaves scenarios are somewhat fanciful ways of formulating logic problems. However, the rigorous treatment of sets happened only in the 19th century due to the german math ematician georg cantor.

You cant tell if he is identifying b or d as knights or knaves. There are 3 individuals, a, b, and c, each of which is either a knight or a knave. Finally, just as you are about to leave the island, you find a group of four islanders named kade, lovelace, maxwell, and nelly, and again you ask what types they are. A says, at least one of us is a knave and b says nothing i dont lie. If you cannot determine what these two people are, can you draw. Knights and knaves puzzles these puzzles have to do with a strange island inhabited by two types of people. You cant tell them apart except by listening to their statements. Book solutions discrete mathematics and its applications.

Knights and knaves in the classroom discrete mathematics. This video was filmed for csci 2824 at the university of colorado. Knights and knaves encounter two people knights always tell the truth knaves always lie figure out whether each person is a knight or a knave from their statements example. Joint mathematics meeting seattle, wa january 7, 2016. Wrote many books on logic puzzles such as alice in puzzleland and to mock a mockingbird most famous for his knights and knaves problem raymond smullyan. This second edition has been developed in response to undergraduate course changes and changes in students needs. A magical island is inhabited entirely by knights who always tell the truth and knaves who always tell lies. Recall that all trolls are either alwaystruthtelling knights or alwayslying knaves. If i want to solve the puzzle and i assume i have two kinds of citizens. If leland and john are both knights, ben could still be lying. Currently he is an assistant professor at the university of northern colorado. Sep 27, 2011 now for the the hardest logic puzzle ever.

The bulletin of mathematics books, issue 43, february, 2003. Discrete mathematics and its applications, global edition 7th edition edit edition. Biggs discrete mathematics has been a bestselling textbook since the first and revised editions were published in 1986 and 1990, respectively. Math 215 discrete mathematics worksheets logic and proof. Therefore, a is a knight,knave, knight and b is also a knight,knave, knight. Inside the mind of a master procrastinator tim urban duration. Graham, discrete mathematics with applications by su. Truth tellers and liars with fewer questions sciencedirect. This is a course note on discrete mathematics as used in computer science.

In this case, john is a knave and bill is a knight. Discrete here is used as the opposite of continuous. While walking through a ctional forest, you encounter three trolls guarding a bridge. W3203 discrete %mathemacs% % logic%and%proofs% spring2015% instructor. Although his primary research interests are in algebraic graph theory and analytic number theory, he is the authoreditor of four books on subjects ranging from the. Discrete mathematics with applications by susanna s. Determine, if possible, what a and b are if they address you in the ways described. You can tell from his gestures that he is saying something about b and d, and that he is trying to use 1 of 4 logical connectives. Find the top 100 most popular items in amazon books best sellers.

Ifais a knight, then we must trust their claim thatbis a knight. These puzzles appear frequently in books of mathematical recre ations. Technically, the first scenario does not strictly lead to a contradiction. Mathematical logic, set theory, the real numbers, induction and recursion, summation notation, asymptotic notation, number theory, relations, graphs, counting, linear algebra, finite fields. Discrete math for computer science students ken bogart dept. John and bill are residents of the island of knights and knaves. Jim says, at least one of the following is true, that joe is a knave or that i am a knight. The first person in the queue said that everybody behind was a knave. On the basis of utterances from some citizens, i must decide what kind they are.

Given their statements below, what can you determine about their identities. This is a tutorial teaching students how to solve knights and knaves problems using propositional statements and truth tables. Cantor developed the concept of the set during his study of the trigonometric series, which is now known as the limit point or the derived set operator. Given you know that at least one of them is a knave, exactly how many are knaves. A is knight so c is knave if a is knave, then b is knight, means a and c are same type. The island of knights and knaves has two types of inhabitants. For example, in terms of propositional logic, the claims, if the moon is made of cheese then basketballs are round, and if spiders have eight legs then sam walks. On the island of knights and knaves, you encounter three inhabitants, a, b, and c. Download it once and read it on your kindle device, pc, phones or tablets.

Knights always tell the truth and knaves always lie. Math 215 discrete mathematics worksheets logic and proof on the island of knights and knaves created by smullyan, knights always tell the truth and knaves always lie. So b must be a knight, but we assumed b was a knave, a contradiction. Knight always tell the truth and knaves always lie. We can also label the three trolls claiming that \3 of us are knights as knights, and the other three as knaves. A very special island is inhabited only by knights and knaves. The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth. A says i am the knight, b says i am the knave, c says i am not the knave. But in this case, both troll 2 and troll 1 would be knaves. But avoid asking for help, clarification, or responding to other answers.

Discrete math knights always tell the truth, knaves always tell a lie and spies can tell the truth or a lie. Use features like bookmarks, note taking and highlighting while reading discrete mathematics. Sep 17, 2003 julian le grand is richard titmuss professor of social policy, london school of economics, and author of motivation, agency and public policy. Jan 01, 1990 however, when read in parallel with rosens book i know, two discrete math books simultaneously is a recipe for insanity it shows its true value. Raymond smullyan collected dozens of puzzles like this in his book, what is the name of this book. Knights and knaves problems to teach logic here are some. Mathematics is concerned with numbers, data, quantity, structure, space, models, and change. Knights, who always tell the truth, and knaves, who always lie. Thanks to alees seehausen who cotaught the discrete mathematics.

Jcac module 2, discrete structures flashcards quizlet. A says i am a knave or b is a knight and b says nothing. One consists of knights, who always tell the truth and the other consists of knaves, who only lie. As you are exploring the island of knights and knaves you encounter two people named a and b a tells you b is a knave. Founded in 2005, math help forum is dedicated to free math help and math discussions, and our math community welcomes students, teachers, educators, professors, mathematicians, engineers, and scientists. Propositional logic studies the ways statements can interact with each other. You can find good hints to the oddnumbered problems at the back of the book which is huge plus if you are self st. A detective has interviewed four witnesses to a crime. Mathematics problem of the week problem number 290 solution hypnotherapist an island is inhabited only by knights and knaves.

Unless otherwise stated, the following propositional variables are used. While walking through a fictional forest, you encounter three trolls guarding a bridge. I have a question regarding knights and knaves and logical proposition. Thanks for contributing an answer to puzzling stack exchange. Maurice kraitchik presents the same puzzle in the 1953 book mathematical recreations, where.

In addition to research in mathematical logic and computability theory, he enjoys recreational. In particular, there must be at least two knights in the group. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. Relate to inhabitants of the island of knights and knaves created by smullyan, where knights always tell the truth and knaves always lie. A logic circuit or digital circuit receives input signals p 1, p 2. Knights and knaves logic puzzles were made popular by the logician and mathematician raymond smullyan. To start the series off, lets have a simple conversation with these knaves and these knights. Of knights and knaves, pawns and queens, published. I have this logic problem that im having trouble with. Discrete math knights always tell the truth, knaves. Knights and knaves is a type of logic puzzle where some characters can only answer questions truthfully, and others only falsely. Knights always tell the truth, and knaves always lie. Thus, ben is a knight, and leland and john are both knaves.

An islander call him a made a statement about himself and a friend, call him b. Discover the best discrete mathematics in best sellers. He was solely responsible in ensuring that sets had a home in mathematics. It is important to remember that propositional logic does not really care about the content of the statements. The island of knights and knaves has just two kinds 6 points of inhabitants.

The name was coined by raymond smullyan in his 1978 work what is the name of this book. I took a discrete math class as part of my computer science minor and here are the two main books my prof recommended. A says, \if im a knight then at least one of us is a knave. View knights and knaves logicpuzzles 2 from cs 1501 at university of pittsburgh. Knights, who always tell the truth, and knaves, who always tell lies. Discrete mathematics for computing mat48 book title discrete mathematics and its applications. From the stories of the witnesses the detective has concluded that. Discrete mathematicsintroduction wikibooks, open books for. Puzzles about knights and knaves truthtellers and liars have a long history as pedagogical devices for understanding classical logic. On the island of knights and knaves you meet two natives, a and b. What are some good books to learn discrete mathematics. Knights, knaves, and logic practice problems online.

A must be a knight,knave, knight and what he said is true,false,true. Relate to inhabitants of the island of knights and knaves cr. On the island of knights and knaves, you are approached by three people, jim, jon and joe. Truthtellers and liars problems also called knights and knaves problems are logic puzzles in which a set of statements is provided, but some of the statements are true and some of the statements are false. A is knave so c is knave is what jamal has answered.

Discrete mathematics kindle edition by chartrand, gary, zhang, ping. Epp explains some things very well but at the end of the day shes a math guru, and as with almost all math gurus ive encountered, she has difficulty packaging complex subjects into digestible. The subject of mathematics is commited to rigorous reasoning. The name was coined by raymond smullyan in his 1978 work what is the name of this book the puzzles are set on a fictional island where all inhabitants are either knights, who always tell the truth, or knaves, who always lie. The trolls will not let you pass until you correctly identify each as. One day 25 of the islanders were standing in a queue. Remember, were still using or inclusively, so when the statement. Feb 16, 2011 discrete math problems knights or knaves. Suppose a says, i am a knave and b is a knight since both knights and knaves claim that that they are knights, but a says that he is a knave and b is a knight, take the second claim, b is knight as false.

Each of the others in the queue said that the person immediately in front of them in the queue was a knave. Discrete mathematics 1, chartrand, gary, zhang, ping. We may determine the correct answer using discrete math. Browse other questions tagged discrete mathematics or ask your own question.

This is consistent with the statements since then only the rst trolls statement is true. Then what b says is false, so it is false that at most two are knaves. Just because john would honestly say that leland is a knight, it does not follow that john has actually said anything about lelands status. Relate to inhabitants of the island of knights and knaves. Alternatively, the two trolls who say \2 of us are knights might be knights and the other four knaves. The aim of this book is not to cover discrete mathematics in depth it should be clear from the description above that such a task would be illde. Since the first part of his statement i am a knave is false,false,true, in order for the whole disjunction this or that to be true, the second part b is a knight ought to be true. Book solutions discrete mathematics and its applications, kenneth h. Knights and knaves problems to teach logic here are some knights and knaves puzzles that might be good for teaching concepts in logic 1. This book aims to raise your confidence in the manipulation and interpretation of formal notations, as well as to train you to solve problems that are fundamentally discrete. Alice tells you, \one of zed and i, exactly one is a knight. American mathematician and musician raymond smullyan named this type of puzzle in his 1978 book what is the name of this book.