# NO VENN DIAGRAMS!

**Discrete Mathematics**Level 2

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.