Question 63
Determine if it is possible to color each of the rational numbers either red or blue such that the following three conditions are all satisfied:
(i) $x$ and $-x$ are opposite colors, for all rational $x \neq 0$;
(ii) $x$ and $1-x$ are opposite colors, for all rational $x \neq 1 / 2$;
(iii) $x$ and $1 / x$ are opposite colors, for all rational $x \neq 0, \pm 1$.
(i) $x$ and $-x$ are opposite colors, for all rational $x \neq 0$;
(ii) $x$ and $1-x$ are opposite colors, for all rational $x \neq 1 / 2$;
(iii) $x$ and $1 / x$ are opposite colors, for all rational $x \neq 0, \pm 1$.