Does there exist a function
such that if
and
are distinct rational numbers satisfying
or
, then
? Justify your answer.
%V0
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.
Školjka