code class$=$"asciimath"$>$Problem $3\mathrm{.}1.$ Prove that for each xin$[$N$]^($s$),$ there is a formula $\backslash$phi $\_($x$)$ such that for any coloring c:$[$N$]^(2)$longrightarrow$\{0,1\},$ it happens that: $()/($bar$)($ u $\_(()$c$))(\backslash$phi $\_($x$))=1$ if and only if c$|\_([$x$]^(2))$ is not constant. $^(2)$