2. Assume that there are three people (A, B, and C) and that there are only two kinds of people:knights, who always tell the truth, and knaves, who always tell lies.IA says: "B is a knave."B says: "A and Care of the same kind."One example of a logically invalid knight-knave setup is when A, B, and C are all knights.Identify all logically valid knight-knave setups for A, B, and C.

Assume that there are three people (A, B, and C) and that there are only two kinds of people:…

Answered: 2. Assume that there are three people…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. Eight different people want to interview for the Defense Against the Dark Arts professorship at Hogwarts: Severus Snape, Tom Riddle, Remus Lupin, Dolores Umbridge, Mad-Eye Moody, Quirinus Quirrell, Barty Crouch, and Gilderoy Lockhart. Albus Dumbledore needs to interview the candidates. How many possible orders are there in which Dumbledore can interview the candidates if all of the following conditions must be simultaneously true? Snape must be interviewed before Riddle, • Dolores Umbridge is interviewed last, • Crouch and Moody must be interviewed at the same time in a joint interview, AND Lupin and Lockhart are interviewed consecutively (although we do not know which of the two is interviewed first)
(The "harem problem") Let B be a set of boys, and suppose that each boy in B wishes to marry more than one of his girl friends. Find a neccessary and sufficient condition for the harem problem to have a solution.(Hint: replace each boy by several identical copies of himself, and then use Hall's theorem.)
A toy shop has 15 airplanes, 15 buses, 17 trains, and 20 bikes in the stock.a. How many ways are there for a person to take 15 toys home if all the airplanes are identical, all the buses areidentical, all the trains are identical and all the bikes are identical?b. How many ways are there for a person to take 15 toys home if all the airplanes are distinct, all the buses aredistinct, all the trains are distinct and all the bikes are distinct?c. How many ways are there for a person to take 25 toys home if all the airplanes are identical, all the buses areidentical, all the trains are identical and all the bikes are identical?
A, B, C, D and E go on a holiday by car. (a) In how many different ways can they choose the seats in the car, if there are any five seats? Order matters. (b) Suppose a car has three back seats. In how many different ways do they can the people sitting in the back seats choose? The order doesn't matter. (c) A has promised to act as a car driver. In how many different ways can the rest of the people choose the seats in the car, if the car has seven seats (in addition to the driver's seat)?
part D E
I don't understand this. Please Helppppp!!!!
A debate team of 4 members is to be formed from a group of 25 students. How many possible teams are possible given the following conditions? a)One of the team members has to be the first speaker, another one has to be the second speaker, a third one has to be the first reply speaker and the other one has to be the second reply speaker. (b) Two of the team members have to be speakers and the two other members of the team have to be reply speakers. (c) No particular role is assigned to any of the students.
A student draws several cards from a deck of 10 unique cards. Which of these statements are true? Select all that apply. There are 120 different ways that 7 cards can be drawn. There are 210 different ways that 4 cards can be drawn. There are 252 different ways that 5 cards can be drawn. There are 240 different ways that 6 cards can be drawn. There are 90 different ways that 8 cards can be drawn.
1) Tom, John, Fred, and Bill are friends whose occupations are (in no particularorder) nurse, secretary, teacher, and pilot. They attended a picnic recently, and eachone brought his favorite meat (hamburger, chicken, steak, and hot dogs) tobarbecue. From the clues provided below, determine each man’s name, occupation,and favorite meat.a) Tom is neither the nurse nor the teacher.b) Fred and the pilot play golf together. The burger lover and the teacher hate golf.c) Tom brought hot dogs.d) Bill sat next to the burger fan, and across from the steak lover.e) The secretary does not play golf.

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