Chained Ratios

Difficulty: Hard · Topics: Discrete Mathematics, Sets, Venn Diagrams

A, B and C are subsets of the universal set E with 21 elements, and

n(Acap B)=n(B)

(n(C))/(7)=(nbig[(Acap C)setminus Bbig])/(2)=n(Bcap C)

(n(C'))/(7)=(n(C'setminus A))/(4)=nbig[(Acap B)setminus Cbig]

What is n(A)?