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Relate to 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 ways described. If you can not determine what these people are, can you draw any conclusions ?

Both $A$ and $B$ say “I am a knight.”
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There are $4$ possible cases :-

Case $1)$ Both $A$ & $B$ are knights

Now, both statements from $A$ and $B$ will be true which will not be contradicting our assumption. So,  Both $A$ & $B$ are knights is a possibility.

Case $2)$ $A$ is knight & $B$ is knave

Now, $A$'s statement "I am a knight" is true which means $A$ is knight and $B$'s statement "I am a knight" is false which means $B$ is knave. Both are not contradicting our assumption.  So, It is also a possible case.

Case $3)$ $A$ is knave & $B$ is knight

Now, $A$'s statement "I am a knight" is false which means $A$ is knave and $B$'s statement "I am a knight" is true which means $B$ is knight. Both are not contradicting our assumption. So, It is also a possible case.

Case $3)$ $A$ is knave & $B$ is knave

Now, $A$'s statement "I am a knight" is false which means $A$ is knave and $B$'s statement "I am a knight" is false which means $B$ is knave. Both are not contradicting our assumption.  So, It is also a possible case.

So, Answer is :- We can't determine what $A$ and $B$ are which means $A$ can either be knight or knave and $B$ can either be knight or knave.

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