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"Every boy has a unique shirt."

Does this mean no two boys share the same shirt, or does it mean no two shirts belong to the same boy?

I suppose the former, but then what is the most succinct way that you would rephrase the latter sentence using the word "unique"?

Is the answer: "Every shirt belongs to a unique boy" ??

I hope this question isn't too silly or trivial.

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    If I meant that no shirt belongs to two boys, I would say "every boy has a *distinct* shirt".2012-08-04

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Closely approximating the English is the following logical formula $\forall b \exists!s P(s,b)$ where $b$ is a boy and $s$ is a shirt, and $P(s,b)$ means that s belongs to b. This means that for each boy there is one and only one shirt that belongs to him. If you want to say that no shirt belongs to two boys you would say $\forall s\exists! b P(s,b),$ and the natural language approximation would be "Every shirt belongs to a unique boy."

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    Yes, my first instinct w$a$s to write that too. ("Every LT, with respect to chosen $b$ases in the domain and $c$odomain, has a unique matrix representation.") Then I wavered and decided that the reader would as well interpret that to mean no two LT (with respect to the same bases) share the same representation, which is patently false!2012-08-04