Quantitative Analysis of Cardinality and Set Operations

\(A\) and \(B\) are two sets. The numbers in the diagram represent the number of elements in each subset. It is given that \(n(A \cap B') = n(A \cap B)\) and \(n((A \cup B)') = n(B)\). Find the value of \(n(B)\).

Venn diagram with sets A and B showing algebraic expressions for element counts