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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 “At least one of us is a knave ” and $B$ says nothing.
in Mathematical Logic by Boss (10.8k points)
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$A$ says "Atleast one of us is a knave".

Case $1)$ Suppose, $A$ is knight

Since, $A$ is knight, So, he always tells the truth. So, here ,  "Atleast one of us is a knave" will be a true statement. Since, $A$ is knight, So, $B$ will be knave.

Case $2)$ Suppose, $A$ is knave

Since, $A$ is knave, So, he always tells lie. So, here ,  "Atleast one of us is a knave" will be a false statement. It means both $A$ and $B$ are knights which is contradicting because $A$ is knave. So, It is not possible here that $A$ is knave.

So, Conclusion :-  $A$ is knight and $B$ is knave.

by Boss (16.4k points)

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