Mathematical Reasoning for Knights and Knaves - myassignmenthelp

Question: Discuss about theMathematical Reasoning for Knights and Knaves. Answer: A very special island is dominated by only knights and knaves. Knights always tell the truth, and knaves always lie. You meet seven inhabitants: Joe, Sue, Sally, Bozo, Dave, Zed and Alice. Joe says that Dave could claim that Alice is a Knave. Sue says that Bozo and Joe are both knights or both knaves. Sally claims, At least one of the following is true: that I am a knight or that Sue is a Knave. Bozo claims, Sally is a knave. Dave claims that Alice is a knight or Bozo is a knight. Zed claims, Of I and Sally, exactly one is a knight. Alice says, Dave could say that Zed is a Knave The task is to determine which of the seven are knights and which are knaves. Solution Alice: Alice says, Dave could say that Zed is a Knave But with regards to Daves claim i.e. Dave claims that Alice is a knight or Bozo is a knight, it clearly implies that Alice is lying since her claim does not concur with Daves Implication: Alice is a knave (knaves always lie) Joe: Joe says that Dave could claim that Alice is a Knave. But with regards to Daves claim i.e. Dave claims that Alice is a knight or Bozo is a knight Taking close analysis of Daves claim, it implies that if Alice is a Knight, then Bozo is a knight or, if Alice is a knave then Bozo is a knight So Joe is telling the truth since his argument act in accordance with Daves claim. Implication: Joe is a knight (knights always tell the truth) Sue: Sue says that Bozo and Joe are both knights or both knaves. Since Joe is a knight, and if Sue is telling the truth (a knight), it would imply Bozo is a knight (since Sue claims that Bozo and Joe are both knights or both knaves) But with regards to Bozos Claim, Bozo claims, Sally is a knave. This Bozos statement would only implying that; If Bozo is a knight, then Sally is a knave since knights always tells the truth, and If Bozo is a knave, then Sally is not a knave (implying Sally is a knight) since knaves always lie. The only implication of the above statement would mean that if Bozo is a knight, then Sally is a knave, or if Bozo is a knave, then Sally is a knight Reviewing Sues statement above, if Sue is telling the truth (a knight), it would imply Bozo is a knight. Superimposing this with Bozos statement implying if he is a knight, then Sally is a knave But with regards to Sallys claim, Sally claims, At least one of the following is true: that I am a knight or that Sue is a Knave. Implying if Sally is a knave, then none of the above statements is true which further implies that sally is a knave and sue is a knight Since the above statement implies Sally is a knave and according to Zeds statement, it would imply that Zed is a knight i.e. Zed claims, Of I and Sally, exactly one is a knight. This Zeds claim would only mean: If Zed is a knight, it would imply Zed is a knight and Sally is a Knave (exactly one) or Sally is a knight and Zed is a Knave, and If Zed is a knave, it would imply both Zed and Sally are knight, or both Zed and Sally are knaves The highlighted statement complies with our argument. Dave on the other hand claims that Alice is a knight or Bozo is a knight, but have analyzed that Alice is a knave and Bozo is a knight implying that Daves claim is true so Dave is a knight From the logical analysis, we have found out that Alice is a knave Joe is a knight Sally is a knave Sue is a knight Bozo is a knight Zed is a knight Dave is a knight NB: A divergent logical analysis would arise if we consider Sue to be lying, which in turn will be ambiguous to analysis since the words both and or are utilized in her statement.