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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?

$A$ says “We are both knaves” and $B$ says nothing.
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Case $1)$ Suppose, $A$ is knight and $B$ can be either knight or knave

So, $A$'s statement "We are both knaves" is true which means $A$ must be knave which is contradicting our assumption. So, It is not a possibility that $A$ is knight.

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

Now, $A$'s statement "We are both knaves" is false which means atleast one should be knight which is not contradicting our assumption that $A$ is knave and $B$ is knight. So, It is a possible case.

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

Now, $A$'s statement "We are both knaves" is false which means atleast one should be knight which is contradicting our assumption. So, It is not a possible case.

So, Answer is $A$ is knave and $B$ is knight.

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