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 \(n[(X-Y)-Z]=50\).

DETAILS AND ASSUMPTIONS


- \(n(A)\) (set cardinality) is the number of elements of set \(A\).

- \(A'\) (set complement) is the set of all elements in \(U\) that are not in \(A\).

- \(A-B\) (set difference) is the set of elements in which all elements of \(A\) that are also in \(B\) are removed.

- \(A \cap B\) (set intersection) is the set of common elements of \(A\) and \(B\).

- NO VENN DIAGRAMS!

- If your get the answer right, you can comment your solution here.

 

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