I Am A KnaveJill says, "Jack is a knight or I am a knave". • Teo : Nel could say I am a knave. Well, so if B is a knave then I am a knave that technically is true if both of them are nights and so he is telling the truth. Another take on this, starting with the knave (and assuming one of each): The knave always lies. Every sentence spoken by a knight is true, and every sentence spoken by a knave is false. “I am the knight” can belong to knight (truth), knave (lie), or spy (lie). Question: This is a problem about an island in which the inhabitants are all either knights or knaves. Troll 3: Either we are all knaves or at least one of us is a knight. Therefore, if A is a knight, both parts of the statement are false, and the middle words "is the same as" makes the statement as a whole true. While walking through a fictional forest, you encounter three trolls guarding a bridge. If A is a knave, the true/false component of each of the statements is different. If one of the natives is a knight and the other one is a knave, they will both answer no to the question. A is a knight and B is a knave. ” – Cannot determine the answer A says, “We are both knaves” and B says nothing. They claim that: • Nel : Teo is a knave. Therefore, A is a knight,knave,knight and B is also a knight,knave,knight. Conversely, a knave will always lie: if a knave states a sentence, then that sentence is false. p∧∼q which is false as A is knave which makes ∼q. This means that he can only say that he is a knight or spy, or that he is not a knave. A must be a knave, and the only way for his statement to be false is for B to be a knight. 1 – A Knight, A Knave and A Spy. (B) A is knave and B is Knight. " Joe tells you, "Peggy is a knight and Zippy is a knave. On the island of knights and knaves and spies, you are approached by three people wearing different colored clothes. (C)Both A and B are knight-This will make our implication false. A says \At least one of us is a knave" and B says nothing. Knights always tell the truth, and knaves always lie. My brother and I are both Knaves. CSE311 Quiz Section: September 27, 2012 1 Introductions 2. A says "At least one of us is a knave" and B says nothing. Suppose A says, "I am a knave but B isn't. Knights always tell the truth and the knaves always lie. b) A says \We are both knaves" and B says nothing. The trolls will not let you pass until you correctly identify each as either a knight or a knave. The first puzzle: Puzzle 0 is contains a single character, A. One among these is a knight, another one a knave, and the third one a spy. Every sentence spoken by a knight is true, and every sentence spoken by a knave is. A knave, a rascal, an eater of broken meats; a base, proud, shallow, beggarly, three-suited, hundred-pound, filthy, worsted-stocking knave; a lily-livered, action-taking knave; a whoreson, glass-gazing, super-serviceable finical rogue; one-trunk-inheriting slave; one that wouldst be a bawd in way of good service; and art nothing but the. The following information should be considered: Troll 3's statement should be true since they can only be knights or knaves, till all of them are knaves, at least one must be a knight. Therefore, the first half of his disjunction ("I am a knave") is false so the second half of if ("B is a knight") must be true. Now let’s represent this in propositional logic. Unfortunately, since Chris is a Knave, there is no way to make the first clause false. " (What are A and B?) Think of this as the compund statement: I am a Knave and B is not a Knave. ' Can you determine who is a knight and who is a knave? 6. " With an "or" statement, only one of the component statements has to be true to make the whole statement true. " The man in red says, "I am a. Since A's answer invariably would be "I'm a knight", it is not possible to determine whether A is a knight or knave from the information provided. If the natives are both knights or both knaves, they will both answer "yes" to the question. Line number A B A says \We are both knaves" 1 Knight Knight F 2 Knight Knave F 3 Knave Knight F 4 Knave Knave T We can eliminate: { Line 1 and 2, as A would be a knight but he lies { Line 4, as A would be a knave, but he says the truth. C says B is a knight or A is a knave. A says: \I am a knave, but B isn't. Similarly, "I am a knave. If B is a knave, then they are not both knights. Logic Puzzles (with Answers) for Adults. This implies that neither is A a knave nor is B . Any role can make that statement, so it eliminates no possibilities of arrangements of knights knaves and spies. What I'm trying to do is check if A is telling the truth or not and then I say A is either a Knight or a Knave. " (What are A and B?) Think of this as the compund statement: I am a Knave and B is not a Knave. Similarly, it cannot be that a native says "I am a knave" because we would then conclude A ≡ ¬A which is always false. The knight always tells the truth. Troll 1: If I am a knave, then there are exactly two knights here. Which type made the following statements, a Knight or a Knave? Explain the reasons for your answers. Peggy claims, "I am a knight or Joe is a knave. " These are very helpful statements, as they always tell us the type of both the speaker and the spoken. 23 relate to inhabitants of the island of knights and knaves created by. Knights always tell the truth_ and knaves always lie. ” or “I am a knave. You meet two inhabitants: Zed and Alice. -21 Both A and B say "I am a knight. Formally, a circular self-referential statement is an equation of the form where are grounded logical propositions (like "I am a Knave"), is a Boolean function, and is a Boolean variable. There can be either a knight or a knave but not both. I'll put the knife in my brain. " What are the true identities of these three men? Hint. ” What are A and B? Ans: Suppose A is a knave. First, Bob can only be either a knave or normal, as a knight cannot truthfully claim to be a normal. You know that one is a knight, one is a knave, and one is a spy. The puzzles involve a visitor to the island who meets small groups of inhabitants. Riddle: Despised I am by knave and liar. These were written by logician Raymond Smullyan. If B is a knave, then they are not both knights. Some More Logic Puzzles (Solution). What I'm trying to do is check if A is telling the truth or not and then I say A is either a Knight or a Knave. A says: \I am a knave, but B isn't. ’” B then says “C is a knave. A is a knight and B is a knave. (B) A is knave and B is Knight If A is knave, then whatever A said need to be complement to get original result since knaves always lie. – A is a knight – B is a knight Both A and B say, “I am a knight. Knight and Knave Problem A says, "I am a knave or B is a knight" and B says nothing. This leaves just 2 ⁄ 3 of the original grid. Can you determine who is a knight and who is a knave? Translate properly first, then show the process of determining. '" B then says "C is a knave. Knight is true, while every statment made by a Knave is false. (B) A is knave and B is Knight If A is knave, then whatever A said need to be complement to get original result since knaves always lie. Zed tells you, “I am a knight or Alice is a knave. knave / knave true. Any role can make that statement, so it eliminates no possibilities of arrangements of knights knaves and spies. (10 points) In the knight/knave model : You meet three inhabitants: Nel, Kusha, and Teo. Therefore, A is a knight and B is a knave. Brook is a Knave Cody is a Knight or Alex is a Knight Brook is a Knave Cody is a Spy If Cody is either the knave or the knight, his answer to the question will be "No", and so the judge will not be able to draw a conclusion. An "Ifthen" statement is false ONLY if the premise is true, but the conclusion is false. Translating an "Either or" statement ….Answer in Discrete Mathematics for assignment #131740. Indeed, if B is telling the truth, then B is a Knight and A is a Knave. If A is a knave, the true/false component of each of the statements is different. "I am a knave" must be true and "B is a knight" must be false. If A says "I am the same type as B". I rise above all death and fire. An example of a knave conjunction, is when A says "B is a knight, or I am a knave," or "C is a knave and I am a knave. ; In the case when Troll 2 is a knight, so Troll 1 is knave, but if that were the case Troll 1's statement should be true, and since knaves do not tell. Case 2: A = knight, B = knave. Lyrics containing the term: knave. One among these is a knight, another one a knave, and the third one a spy. 4) A is a knight and B is a knave. A says "I am a knave or B is a knight" and B says nothing. So complement of p→q p→q is p∧∼q p∧∼q which is false as A is knave which makes ∼q ∼q false. Math 311 Project 2 Handout Instructions. ’ Alice claims, ‘It’s not the case that Zed is a. However, this contradicts what A said ("Either A is a knave or B is a knight"). Every sentence spoken by a knight is true, and every sentence spoken by a knave is false. If A says "I am a knight" then what we can infer from the statement is A ≡ A. C then says "A is knight". So A must be a KNAVE lying. If B is a knight, then they are both knights. Each is either a knight, who always tells the truth, or a knave, who always lies. Question: This is a problem about an island in which the inhabitants are all either knights or knaves. Abe says, 'At least one of the following is true: that Carol is a knave or that I am a knight. If A says “I am a knight” then what we can infer from the statement is A ≡ A. If B says "A is a Knave", then you can conclude that A and B are of different "type" (Knight or Knave). A says "At least one of us is a knave" and B says nothing. An islander - call him A - made a statement about himself and a friend, call him B: "Either I am a knave or B is a knight. i am a knave or b is a knight. Which type made the following statements, a Knight or a Knave? Explain the reasons for your answers. The Knave would lie and tell you the opposite direction of Freedom, and the Knight will then tell you what the Knave would. You meet two inhabitants: Zed and Peggy. Knights always tell the truth and the knaves always lie. A GENERAL METHOD OF SOLVING SMULLYAN'S PUZZLES. Tim says, "I am a Knave, but Grace isn't. Another take on this, starting with the knave (and assuming one of each): The knave always lies. You also know that one path leads to freedom, and the other path. Both A and B say \I am a knight" Either one could either thing. Neither of the people is a Normal. Jim says, "at least one of the following is true, that Joe is a knave or that I am a knight. Each troll makes a single statement: Troll 1: If I am a knave, then there are exactly two knights here. If B says "A is a Knave", then you can conclude that A and B are of different "type" (Knight or Knave). There are three people (Alex, Brook and Cody), one of whom is a knight, one a knave, and one a spy. Now since we know that (I am knave = false) OR (b is knight = unknown) = true B must be a knight to make the OR evaluate to true, since the other input is false. If John is a knight then Bill can be neither a knight nor a knave (either would make Bills statement self-contradictory), yet if John is a knave Bill's statement is consistent no matter what he is. A Note on Knights, Knaves, and Truth Tables. Vasu says: "Shyam is a knave. A says, “If B is a knight then I am a knave. Knave Conjunctions An example of a knave conjunction, is when A says "B is a knight, or I am a knave," or "C is a knave and I am a knave. Therefore, A can either be a knave or a knight, and B is always a knave. A very special island is inhabited only by knights and knaves. Here is my proof: The statement is "If Bill is Knight, then I am a Knight". Born on September 11, 1938, in Ft. Each troll makes a single statement:. % Example 1: You meet two inhabitants, A and B. A says either “I am a knight. Peggy claims, "I am a knight or Joe is a knave. If B is a knave, then they are not both knights. Since A's answer invariably would be "I'm a knight", it is not possible to determine whether A is a knight or knave from the information provided. On the island of knights and knaves, you come to a fork in the road with one man standing before each path. Red says, “I am a knight. Solved The following refer to Smullyan's “knights and. You know that one of them is a knight, and the other is a knave. B then adds "C is a knave'. If A is a knight, then B must be a knave. (B) A is knave and B is Knight. Therefore, A is a knight and B is a knave. ’” B then says “C is a knave. If A is a knave, the true/false component of each of the statements is different. A says "We are both knaves" and B says nothing. On the island of knights and knaves, you are approached by three people, Jim, Jon and Joe. A says "I am a knave or B is a knight" and B says nothing. They claim that: • Nel : Teo is a knave. A says: I am both a knight and a knave. We first prove an auxiliary law: P ↔ P ∨ Q. 3) A and B are knaves and knights, respectively. ; In the case when Troll 2 is a knight, so Troll 1 is knave, but if that were the case Troll 1's statement should be true, and since knaves do not tell the truth. Troll 2: Knave. To solve the puzzle, note that no inhabitant can say that he is a knave. Here's the basic syntax: Implication ("Whatever a says", "A is a knight") Implication (Not ("Whatever a says"), "A is a Knave"). Puzzle 0 contains a single character, A. Knave Conjunctions An example of a knave conjunction, is when A says "B is a knight, or I am a knave," or "C is a knave and I am a knave. Alex says: "Cody is a knave. A must be a knight,knave,knight and what he said is true,false,true. An islander - call him A - made a statement about himself and a friend, call him B: "Either I am a knave or B is a knight. Yep, time for logic problems again. ” Green says, “I am the spy. The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth. Similarly, it cannot be that a native says “I am a knave” because we would then conclude A ≡ ¬A which is always false. Here is my proof: The statement is "If Bill is Knight, then I am a Knight". This means that he can only say that he is a knight, or that he is not a knave or spy. In that table, there are four possible truths; (i) A and B are knights, (ii) A is a knight and B is a knave, (iii) A is a Knave and B is a knight, and (iv) A and B are knaves. A says "At least one of us is a knave" and B says nothing. Perhaps your experience with mathematics so far has mostly involved finding. The Paradox: I am not a knight. Therefore, the first half of his disjunction ("I am a knave") is false so the second half of if ("B is a knight") must be true. Which troll is which? In order to do mathematics, we must be able to talk and write about mathematics. A says "The two of us are both knights" and B says "A 20. Usually the aim is for the visitor to deduce the inhabitants'. - A is a knight - B is a knight Both A and B say, "I am a knight. A says, “I am a knave or B is a knight” and B says nothing. Knights always tell the truth, knaves always lie. Thus, his statement must be false. Jim says, "at least one of the following is true, that Joe is a knave or that I am a knight. Knights always tell the truth; Knaves always lie; Spies can either lie or tell the truth ; A says: I am a knight; B says: That is true. A knave, a rascal, an eater of broken meats; a base, proud, shallow, beggarly, three-suited, hundred-pound, filthy, worsted-stocking knave; a lily-livered, action-taking knave; a whoreson, glass-gazing, super-serviceable finical rogue; one-trunk-inheriting slave; one that wouldst be a bawd in way of good service; and art nothing but the. They're pretty simple, so you can feel all "smurt" for figuring them. /Name/F4 Therefore they are a spy. Knights always tell the truth, so they cannot say "I'm a knave". John didn't say "Bill is a knave and I am not a knight" (contrary to what the boolean algebra states). Knave: I do Play the Knave first will be submitted to Steam Greenlight, a service that allows Steam users to vote on games they would like to see added to the platform Campagnolo 68x110 Italiana Knight and Knave Problem A says, "I am a knave or B is a knight" and B says nothing Knight and Knave Problem A says, "I am a knave or B is a. Knights and Knaves is a type of logic puzzle where some characters can only answer questions truthfully, and others only falsely. CASE 1: Both will always be truthful. Each troll makes a single statement: Troll 1: If I am a knave, then there are. 3: Propositional Logic — Solutions. Is There Gold on This Island? On a certain island of knights and knaves, it is rumored that there is gold buried . A is a knave. This means that he can only say that he is a knight or spy, or that he is not a knave. A says \I am a knave or B is a knight" and B says nothing. The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth. " In each of the above puzzles, each character is either a knight or a knave. knave Wet earth carved from tributaries Terrifies me count the miles Once you've seen this clearing before Get your shit straight count the miles Tall. B says if A is a night that I am a knight. However, this contradicts what A said ("Either A is a knave or B is a knight"). This means that he can only say that he is a knight or spy, or that he is not a knave. Knights must tell the truth. Red and Blue There are two people standing in front of you, Red and Blue. Troll 3: Either we are all knaves or at least . Case 3: A = knave, B = knight. Answer: This leads to four possibilities, agreeing with Trenin’s conclusion. So John would have to be a knave or we would. "I am a knave" must be true and "B is a knight" must be false. On the other hand, Cody can answer "Yes" only if he is the spy. • Teo : Nel could say I am a knave. B says “A said ‘I am a knave. One among these is a knight, another one a knave, and the third one a spy. There are many variations of this puzzle, but most involve asking a question to figure out who is the knight and who is the knave. Alex says: "I am not a spy. Therefore, A is a knave. If A says “I am a knight” then what we can infer from the statement is A ≡ A. "I am a knave" must be true and "B is a knight" must be false. As mentioned in comments, both a Knight and a Knave can say "I am a Knight" so A's statement gives no information. One wears blue, one wears red, and one wears green. A cannot be a knight since by his own testimony he would then be. knight and knave problem logic puzzle 4,964 For part (a), the answer is yes. Here's the basic syntax: Implication ("Whatever a says", "A is a knight") Implication (Not ("Whatever a says"), "A is a Knave"). A says "We are both knaves" and B says nothing. Read Shakespeare's 'O, What A Rogue And Peasant Slave Am I' soliloquy from Hamlet below with modern English translation and analysis, plus a video . KNAVE because it's false. ’” B then says “C is a knave. You can only conclude that one is a Knight and the other a Knave, but not which one among A and B is the Knight. Similarly, it cannot be that a native says “I am a knave” because we would then conclude A ≡ ¬A which is always false. A is a knave. – A is a knight – B is a knight Both A and B say, “I am a knight. But if he is lying, he has to be a Knave, and A is a. So this is how I check if what they "SAY" is correct or not and I assign corresponding roles. The first puzzle: Puzzle 0 is contains a single character, A. The first is a knight, the second is a knave. Knights always tell the truth and knaves always lie. Let's proceed with testing whether (i) is true or false. and knaves created by Smullyan, where knights always tell the truth and knaves always lie. What is the least number of socks so I am sure to have two matching pairs? Answer: 5. If A is knave, then whatever A said need to be complement to get original result since knaves always lie. They are brought before a judge who wants to identify the spy. Answer: This leads to four possibilities, agreeing with Trenin's conclusion. Knave: I do Play the Knave first will be submitted to Steam Greenlight, a service that allows Steam users to vote on games they would like to see added to the platform. 68 In this video, we discussed this . Conversely, a knave will always lie: if a knave states a sentence, then that sentence is false. B then adds "C is a knave'. -21 Both A and B say "I am a knight. Troll 3: Either we are all knaves or at least one of us is a knight. So A must be a KNAVE lying about B which makes B a KNAVE as well. I think the correct answer to #2 is that it is impossible to determine who is a knight and who is a knave. “I am a knave or B is a knight. The man in blue says, "I am not a spy. A says “I am a knave or B is a knight” and B says nothing. A visitor in the island meets three people A, B, and C. A very special island is inhabited only by knights and knaves. If A says “I am the same type as B”. Suppose A says, “I am a knave, but B isn't”. Since all 3 persons cannot be neither knights, nor knaves, they are spies. B then adds "C is a knave'. 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. ” In each of the above puzzles, each. % A says: "Either I am a knave or B is a knight. There are two more variations of this problem, solution to which , I am not able to figure out yet. Possible arrangements: TFS, TSF, FTS, FST, SFT, STF. Jack the knave Jack of Spades How to behave Jack of all trades Jack of all trades but master of none Your life is a mess what's going on You show. A says either “I am a knight. Every sentence spoken by a knight is true, and every sentence spoken by a knave is false. Knights always tell the truth, while knaves always lie. As mentioned in comments, both a Knight and a Knave can say "I am a Knight" so A's statement gives no information. Three inhabitants A, B, C meet some day, and A says either "I am a knight" or "I am a knave”, we don't yet know which. John didn't say "Bill is a knave and I am not a knight" (contrary to what the boolean algebra states). Knight and Knave Problem A says, “I am a knave or B is a knight” and B says nothing. If A is a knight, then B must be a knave. But if he is lying, he has to be a Knave, and A is a. 1 - A Knight, A Knave and A Spy. " Brook says: "I am a spy. Bob said: Both Chris and I (Bob). The trolls will not let you pass until you correctly identify each as either a knight or a knave. A says "I am a knave or B is a knight" and B says nothing. Each is either a knight, who always tells the truth, or a knave, who always lies. Puzzle 2 has two characters: A and B. This means that he can only say that he is a knight, or that he is not a knave or spy. You meet three inhabitants: Peggy, Joe and Zippy. What Is the Name of This Book? revd. Any islander who says "or I am a knave" will be making a statement that must be, overall, truthful and is therefore a knight, while any islander who says "and I am a knave" will by lying, and must be knave. -21 Both A and B say "I am a knight. where knights always tell the truth and knaves always lie. Brainstorming Puzzles Set 7. The two priests made the following statements: First Priest: I am a knave, and I don't know why there is something instead of nothing. Answer: This leads to four possibilities, agreeing with Trenin’s conclusion. Case 1: A = knight, B = knight. One wears blue, one wears red, and one wears green. A says \At least one of us is a knave" and B says nothing. B then adds "C is a knave'. Since A's answer invariably would be "I'm a knight", it is not possible to determine whether A is a knight or knave from the information provided. Raymond M Smullyan book Knights and Knaves. " Joe tells you, "Peggy is a knight and Zippy is a knave. Knights always tell the truth, knaves always lie. Each is either a knight, who always tells the truth, or a knave, who always lies. You know that one is a knight, one is a knave, and one is a. Now add the wrinkle of language difficulties. ’ Can you determine who is a knight and who is a knave? 6. • Kusha : It is false that Nel is a knave. On the island of knights and knaves, you come to a fork in the road with one man standing before each path. For part (b), there is always an odd number of knights. Check! "Mel says, `Neither Zoey nor I are knaves. A cannot be a knight since by his own testimony he would then be a knave. Knight and knave problem a says the two of us are. " Puzzle 3 has three characters: A, B, and C. Any islander who says "or I am a knave" will be making a statement that must be, overall, truthful and is therefore a. A says \At least one of us is a knave" and B says nothing. If one of the natives is a knight and the other one is a knave, they will both answer no to the question. b) A says \We are both knaves" and B says nothing. Therefore, we get that both A and B ar knights. I Rise Above All Death And Fire. Knights always tell the truth, and knaves always lie. A says \We are both knaves" and B says nothing. A spy can either tell the truth or lie. An islander - call him A - made a statement: "Either I am a knave or 2 + 2 = 5. A says \The two of us are both knights" and B says \A is a knave" A is a knave and B is a knight. Indeed, if B is telling the truth, then B is a Knight and A is a Knave. You can only conclude that one is a Knight and the other a Knave, but not which one among A and B is the Knight As mentioned in comments, both a Knight and a Knave can say "I am a Knight" so A's statement gives no information. The following information should be considered: Troll 3's statement should be true since they can only be knights or knaves, till all of them are knaves, at least one must be a knight. If A is a knight, then B must be a knave. We encounter two people; A ad B Determine. with just a single character named A. A knave, a rascal, an eater of broken meats; a base, proud, shallow, beggarly, three-suited, hundred-pound, filthy, worsted-stocking knave; a lily-livered, action-taking knave; a whoreson, glass-gazing, super-serviceable finical rogue; one-trunk-inheriting slave; one that wouldst be a bawd in way of good service; and art nothing but the. We again have three inhabitants, A, B and C, each of whom is a knight or a knave. Peggy claims, "I am a knight or Joe is a knave. For example, consider a simple puzzle with just a single character named A. November 7: Logic To solve logic puzzles it helps to think about all. ” Cody says: "I am the spy. There are many variations of this puzzle, but most involve asking a question to figure out who is the knight and who is the knave. A says \I am a knave or B is a knight" and B says nothing. A says "I am both a knight and a knave. A knave, a rascal, an eater of broken meats; a base, proud, shallow, beggarly, three-suited, hundred-pound, filthy, worsted-stocking knave; a lily-livered, action-taking knave; a whoreson, glass-gazing, super-serviceable finical rogue; one-trunk-inheriting slave; one that wouldst be a bawd in way of good service; and art nothing but the. A is a knave, and B (speaking truthfully) is therefore a knight. Every sentence spoken by a knight is true, and every sentence spoken by a knave is. Formally, a circular self-referential statement is an equation of the form where are grounded logical propositions (like "I am a Knave"), is a Boolean function, and is a Boolean variable. There are three people (Vasu, Ram and Shyam). The trolls will not let you pass until you correctly identify each as either a knight or a knave. Zed tells you, 'Alice could say that I am a knight. While walking through a fictional forest, you encounter three trolls guarding a bridge. The only way to make it false is to make the first clause ("both Bob and I are not Knaves") true and the second clause ("all of Alice, Bob, and I are Normals") false. if possible, what A and B are if they say the following: A says "I B is a knave, then aIII kuave" ad B says "Il A is a knight , then AM knight, Discussion You must be signed in to discuss. Lets say Chris is a Knave. we infer A ≡ (A ≡ B) which simpliﬁes to B. 1 – A Knight, A Knave and A Spy. There are four scenarios: 1) Both A and B are knights. If A is a knight, then B must be a knave. MAT1348: Knights and Knaves. " Who is really the knight and who is the knave? Solution It's impossible for Blue to be the knight. ” Puzzle 1 has two characters: A and B. See this puzzle without solution. As mentioned in comments, both a Knight and a Knave can say "I am a Knight" so A's statement gives no information. You know that one is a knight, one is a knave, and one is a spy. If I am a knave, then the right fork will take you to the city. Either I am a knave or Q is a knight. If both A and B are knights, then the statement by A that "I am either a knave or B is. Therefore, A is a knight and B is a knave. ” Blue says, “Red is telling the truth. Therefore, A can either be a knave. Many a duteous and knee-crooking knave that, doting on his own obsequious bondage, wears out his time, much like his master's ass, For naught but provender, and when he's old - cashier'd! Whip me such honest knaves. Now since we know that (I am knave = false) OR (b is knight = unknown) = true B must be a knight to make. What I'm trying to do is check if A is telling the truth or not and then I say A is either a Knight or a Knave. Blue says, "We are both knaves. Peggy tells you, ‘Either Zed is a knight or I am a knight. A says "If B is a knight, then I am a knave", B says nothing. ' Alice claims, 'It's not the case that Zed is a. we infer A ≡ (A ≡ B) which simpliﬁes to B. Another take on this, starting with the knave (and assuming one of each): The knave always lies. – A is a knave – B is a knight A says, “B is a knight” and B says, “The two of us are opposite types. Vasu says: “Shyam is a knave. On the island of knights and knaves and spies, you are approached by three people wearing different colored clothes. I'm having quite a bit of difficulty trying to figure out how to represent the fact that a knight will always tell the truth and a knave will always lie using propositional logic. Indeed, if B is telling the truth, then B is a Knight and A is a Knave. This is the truth (Mel is a knave), which is what we expect, since Zoe is a Knight. (B) A is knave and B is Knight If A is knave, then whatever A said need to be complement to get original result since knaves always lie. So A must be a KNAVE lying about B which makes B a KNAVE as well. " Puzzle 1 has two characters: A and B. " Cody says: "I am the spy. Thinking of me for trillions of years, And dreaming me for billions of years, Wrote and found me ugly, Your failure! If not lovely? Erase, write another one, no crocodile tears!. Zed tells you, ‘Alice could say that I am a knight. Zed says that Peggy is a knave. The Paradox: I am not a knight. " or "I am a knave. A says: \I am a knave, but B isn't. “Suppose A says, 'Either I am a knave or B is a knight. King Lear Act 2, Scene 2 Translation. A very special island is inhabited only by knights and knaves. Well let's check is A and night, yes, but then that should imply B as a night, but B is also a night. Troll 1: If I am a knave then there are exactly two knights here. An example of a knave conjunction, is when A says "B is a knight, or I am a knave," or "C is a knave and I am a knave. A says either "I am a knight. A says either “I am a knight. • Kusha : It is false that Nel is a knave. Peggy tells you, 'Either Zed is a knight or I am a knight. " Zippy says, "I and Joe are different. " Zippy says, "I and Joe are different. Exactly one of of them is a knight, one normal and one a knave. Knight is true, while every statment made by a Knave is false. If B says "A is a Knave", then you can conclude that A and B are of different "type" (Knight or Knave). A says \I am a knave or B is a knight" and B says nothing. As a result, A is telling the truth while B is lying, which is impossible. A dubious one-statement solution to the problem is: "If I am not a knave, . —————————————————— I know the solution right away. Alex says: "Cody is a knave. Jim says, "at least one of the following is true, that Joe is a knave or that I am a knight. On the island of knights and knaves and spies, you are approached by three men. We say that such a statement is True if. 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. Implementing Knights and Knaves using Artificial Intelligence in. NewsBreak provides latest news, comment and analysis on celebrity obituaries and death in Hazel Park, MI. Therefore, A is a knave. If the person you ask is a Knight, then the other person is a Knave. ” or “I am a knave. So the truth table for that statement is A/B 1. Therefore A is lying and A is a knave. Well, so if B is a knave then I am a knave that technically is true if both of them are nights and so he is telling the truth. Can you determine who is a knight and who is a knave? Translate properly first, then show the process of determining. September 11, 1938 - October 9, 2019. I think the correct answer to #2 is that it is impossible to determine who is a knight and who is a knave. He cannot be a knave and must be a knight. BOTH: KNIGHT because it's true, KNAVE because he lies. A says: “Either I am a knave or B is a knight”. While walking through a fictional forest, you encounter three trolls guarding a bridge. A says “I am a knave and B is a knight” and B says nothing. If A says “I am a knight” then what we can infer from the statement is A ≡ A. ” (d) A says: “I am a knight or B is a knave. In a remote island, everyone 1s either knight or kuave. Hazel Juanita Carter, 81, of Lake Park, died on Wednesday, October 9, 2019, at Berrien Nursing Center in Nashville. So complement of p→q p→q is p∧∼q p∧∼q which is false as A is knave which makes ∼q ∼q false. Three inhabitants A, B, C meet some day, and A says either "I am a knight" or "I am a knave”, we don't yet know which. Despised am I by knave and liar, After me, the wise inquire. Knight and Knave Problem A says, “I am a knave or B is a knight” and B says nothing. In a remote island, everyone 1s either knight or kuave. Problem 1 : King can ask two different yes/ . I'm having quite a bit of difficulty trying to figure out how to represent the fact that a knight will always tell the truth and a knave will always lie using propositional logic. A says “I am both a knight and a knave. A says either “I am a knight. Knights and Knaves 2: an outline solution to a simple word. • If I am a knave, then B is a knight. To solve the puzzle, note that no inhabitant can say that he is a knave. If John is a knight then Bill can be neither a knight nor a knave (either would make Bills statement self-contradictory), yet if John is a knave Bill's statement is consistent no matter what he is. A says \We are both knaves" and B says nothing. LOGIC PROBLEM (KNIGHTS, KNAVES AND SPIES) #rolandoasisten || MATHEMATICS OF THE MODERN WORLD | VIDEO NO. If A is knave, then whatever A said need to be complement to get original result since knaves always lie. B says if A is a night that I am a knight. Conversely, a knave will always lie: if a knave states a sentence, then that sentence is false. Zed says that Peggy is a knave. ” In each of the above puzzles, each character is either a knight or a knave. Riddle of the Week #45: Knights and Knaves, Part 3. A is a knight and B is a knave. Therefore, the first half of his disjunction ("I am a knave") is false so the second half of if ("B is a knight") must be true. A says \The two of us are both knights" and B says \A is a knave" A is a knave and B is a knight. Two people, Red and Blue, stand before you. Each troll makes a single statement: Troll 1: If I am a knave, then there are. ” With an “or” statement, only one of the component statements has to be true to make the whole statement true. Alex says: "Cody is a knave. ” In each of the above puzzles, each character is either a knight or a knave. knight and knave problem logic puzzle 4,964 For part (a), the answer is yes. After me, the wise inquire, I rise above all death and fire. If the natives are both knights or both knaves, they will both answer "yes" to the question. A can’t be both a knight and a knave. Knights and Knaves Puzzles. (10 points) In the knight/knave model : You meet three inhabitants: Nel, Kusha, and Teo. Knights and Knaves ( clp(b) ). ” Cody says: "I am the spy. ; A tricky, deceitful fellow; a dishonest person. As a visitor, you came upon two inhabitants which we will call A and B. On the island of knights and knaves, you are approached by three people, Jim, Jon and Joe. Vasu says: “Shyam is a knave. ” B says: “A would tell you that I am a knave. if possible, what A and B are if they say the following: A says "I B is a knave, then aIII kuave" ad B says "Il A is a knight , then AM knight, Discussion You must be signed in to discuss. Betty tells you, `I know that I am a knight and that Sally is a knave. Case 3: A = knave, B = knight. This means that he can only say that he is a knight, or that he is not a knave or spy. Three inhabitants A, B, C meet some day, and A says either "I am a knight" or "I am a knave", we don't yet know which. The knight never tells a lie, the knave never tells the truth, and the spy can either tell the truth or he can lie. A is a knave, and B (speaking truthfully) is therefore a knight. Try and convince yourself of that. " - Cannot determine the answer A says, "We are both knaves" and B says nothing. Our statements are SA= Xor[C, ~A], SB= Xor[A, ~BJ, and Xor[(B I I ~ . Knights and Knaves 2 Puzzle. If John is a knight then Bill can be neither a knight nor a knave (either would make Bills statement self-contradictory), yet if John is a knave Bill's statement is consistent no matter what he is. You know that one of them is a knight, and the other is a knave. First, Bob can only be either a knave or normal, as a knight cannot truthfully claim to be a normal. " Joe tells you, "Peggy is a knight and Zippy is a knave. You know that one is a knight, one is a knave, and one is a spy. Case 3: A = knave, B = knight. Red says, "We are both knaves. You meet two inhabitants: Zed and Peggy. The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth. Therefore, if A is a knight, both parts of the statement are false, and the middle words "is the same as" makes the statement as a whole true. " (What are A and B?) Think of this as the compund statement: I am a Knave and B is not a Knave. Therefore, B's statement must be untrue, so he is a knave, making C's statement true, so he is a knight. You know that one is a knight and one is a knave, but you don't know which is which. As mentioned in comments, both a Knight and a Knave can say "I am a Knight" so A's statement gives no information. q: I am a knave (Means A is a knave) p→q (A) A is a knight and B is a knave If A is knight, then we can take the given implication as said by A in it's original form since Knights. Troll 1: If I am a knave, then there are exactly two knights here. Every sentence spoken by a knight is true, and every sentence spoken by a knave is. " C says "A is a knight. Troll 1: If I am a knave, then there are exactly two knights here. A says "We are both knaves. On the island of Logica, there are Knights and Knaves. B says “A said ‘I am a knave. The knight never tells a lie, the knave never tells the truth, and the spy can either tell the truth or he can lie. On the island of knights and knaves, you are approached by three people, Jim, Jon and Joe. Common Logic Puzzles – The Knights and Knaves, …. If A says “I am the same type as B”. What are A and B? Solution: Suppose that A lies. ' Bess says, 'Abe could claim that I am a knave. John didn't say "Bill is a knave and I am not a knight" (contrary to what the boolean algebra states). Pierce, Florida, she was a daughter of the late Benjamin Carroll. We say that such a statement is True if setting True makes the equation hold, and similarly say it is False if False is a solution. So John would have to be a knave or we would. Thinking of me for trillions of years, And dreaming me for billions of years, Wrote and found me ugly, Your failure! If not lovely? Erase, write another one, no crocodile tears!. A says \The two of us are both knights" and B says \A is a knave" A is a knave and B is a knight. If knave say "I'm a knave" it will be truth, so knaves have say only "I'm a knight". If both the premise and the conlcusion are false, the statement is true. NEITHER because the Knight wouldn't tell a lie and the KNAVE wouldn't be able to tell the truth. Solved While walking through a fictional forest, you. " This statement means that A must be a spy, since neither a knight nor a knave. "I am a knight" or "I am not a knave". But since this is always true we get no information from the statement. 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. " This statement means that A must be a spy, since neither a knight nor a knave. Therefore, B's statement must be untrue, so he is a knave, making C's statement true, so he is a knight. Each troll makes a single statement: Troll 1: If I am a knave, then there are. " The man in red says, "I am a. Both A and B say \I am a knight" Either one could either thing. (c) A says: “We are either both knights or both knaves. There's no way the speaker can be a Knight, since the ¯rst part of the statement is false. I'm having quite a bit of difficulty trying to figure out how to represent the fact that a knight will always tell the truth and a knave will always lie using propositional logic. Viewed 735 times. Therefore, the first half of his disjunction ("I am a knave") is false so the second half of if ("B is a knight") must be true. "I am a knave or B is a knight. Any islander who says "or I am a knave" will be making a statement that must be, overall, truthful and is therefore a knight, while any islander who says "and I am a knave" will by lying, and must be knave. Knights always tell the truth and knaves always lie.