# NO VENN DIAGRAMS!

Let $$X$$, $$Y$$ and $$Z$$ be three distinct subsets of the universal set $$U$$, no two of which are disjoint.

WITHOUT USING VENN DIAGRAMS, find $$n(X)$$, given: $$n(X \cap Y \cap Z) = 5$$, $$n[X \cap (Y - Z)]=20$$, $$n[X \cap (Z - Y)]=25$$, and $$n[(X-Y)-Z]=50$$.