Posted by **Sam** on Tuesday, January 16, 2007 at 7:23pm.

This exercise relate to the inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, A and B. Determine, if possible, what A and B are if they address you in the way described. If you cannot determine what these two people are, can you draw any conclusions?

A says “The two of us are both knights”, and B says “A is a knave”.

part 2:

A says:if B is a knave, then I am a knight

B says: we are different

Who is who?

If A says we are both knights, then you know that he is lying because both can't be.

In part two which is the only statement that can be true?

If A is a liar, then both are not knights, and A is a knave.

If B is the liar, then A is a knight.

let a be knave, b be knave, A be knight, B Knight.

IF Then

a ab or aB

b Ab

A AB

B aB

Conclusions. cant be Ab, or AB, or aB

Think out why.

Part II

A can be Ab or AB

a can not be Ab

B aB or Ab

b ab

check my thinking.