Is the following relation on disjoint subsets of [n] transitive?
Solution 1:
As suggested in the comments; consider the sets \begin{eqnarray*} A&=&\{2,4,9\},\\ B&=&\{3,5,7\},\\ C&=&\{1,6,8\}. \end{eqnarray*}
As suggested in the comments; consider the sets \begin{eqnarray*} A&=&\{2,4,9\},\\ B&=&\{3,5,7\},\\ C&=&\{1,6,8\}. \end{eqnarray*}