Let $X$ be a set with $|X| = n$ , and let $X_1 , X_2 ,... X_n$ be the $n$subsets eith $|X_j| \geq 2$, for $1 \leq j \leq n$. Suppose for each $2$ element subset $Y$ of $X$, there is a unique $j$ in the set $1,2,3....,n$ such that $Y \subset X_j$ . Prove that $X_j \cap X_k \not= \Phi$ for all $1 \leq j < k \leq n$