# Logic

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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.

• Logic -

A is knave
Bis knight

because from second statement it is true that both are different.
if so, the statement by A is lie.
so the one who lie is a knave that means A IS KNAVE. As both can't be same obviously the other is knight means B IS KNIGHT

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