In a set $X$ of n people, some know each other and others do not, where the relationship to know is symmetric; that is, if $A$ knows $B$. then $B$ knows $A$. On the other hand, given any$4$ people: $A, B, C$ and $D$: if $A$ knows $B$, $B$ knows $C$ and $C$ knows $D$, then it happens at least one of the following three: $A$ knows $C, B$ knows $D$ or $A$ knows $D$. Prove that $X$ can be partition into two sets $Y$ and $Z$ so that all elements of $Y$ know all those of $Z$ or no element in $Y$ knows any in $Z$.