Please show all steps and use the same numbers shown in the problem so that I ca

Question

Please show all steps and use the same numbers shown in the problem so that I can follow along easily. Thank you.

9. Three people (X, Y, Z) are in a room with vou. One is a knight (knights always tell the truth), one is a knave (knaves always lie), and the other is a spy (spies may either lie or tell the truth). X says "I am not a spy.", Y says “X is a knave.", and Z says "Y is a spy." Which of the following correctly identifies all three people? A. X is the spy. Y is the knave.Y is the knave. Z is the knight. Z is the spy. Xis the knight Y is the spy. Z is the knave. Xis the knave. Y is the spy. Z is the knight. X is the knight. X is the spy. Y is the knight. Z is the knave.

Explanation / Answer

Option (C) is correct.

Explanation:

(A): says that X is the spy, and Y is the knight. If Y is Knight then he will always speek truth, but in question Y says "X is knave", but in option A, X is identified as spy. Thus wrong.

(B) says that X is the spy, Y is the knave, and Z is knight. If Z is Knight then he will always speek truth, but in question Z says "Y is spy", but in option A, Y is identified as knave. Thus wrong.  

(D): Z is identified as knave, thus he will always lie, and in question Z says, "Y is a spy". Thus Y should not be a spy. But in option Y is a spy Thus wrong.

(E): X is identified as knave, thus he must lie and in question X says, "I am not a spy", and a knave always lie, so he must be a spy. which is wrong and contradictory to given option.

(C): X is the knight, thus always speaks truth. In question says, "I am not a spy". which is a truth. Y is the knave, thus always lie, says in question, "X is knave", which is a lie, as X is given a knight. Z is the spy, thus may either lie or tell the truth, which is also correct.

Thus option (C) correctly identifies the X,Y, and Z.

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