NO VENN DIAGRAMS!

Probability Level 2

Let XX, YY and ZZ be three distinct subsets of the universal set UU, no two of which are disjoint.

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

DETAILS AND ASSUMPTIONS


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

- AA' (set complement) is the set of all elements in UU that are not in AA.

- ABA-B (set difference) is the set of elements in which all elements of AA that are also in BB are removed.

- ABA \cap B (set intersection) is the set of common elements of AA and BB.

- NO VENN DIAGRAMS!

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

 

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