Does there exist a function such that if and are distinct rational numbers satisfying or , then ? Justify your answer.
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Does there exist a function $s\colon \mathbf{Q} \rightarrow \{-1,1\}$ such that if $x$ and $y$ are distinct rational numbers satisfying ${xy=1}$ or ${x+y\in \{0,1\}}$, then ${s(x)s(y)=-1}$? Justify your answer.
Source: Međunarodna matematička olimpijada, shortlist 2004
Školjka 
such that if 
and 
are distinct rational numbers satisfying 
or 
, then 
? Justify your answer.