Sets

A Venn diagram has \(B\subset A\), with both sets inside \(\xi\).
You are given:
\[n(A)=3x+4,\qquad n(B)=x+2,\] \[n(A')=8,\qquad n(A\cap B')=18.\]

1. Draw a diagram showing the relationship between the sets.

2. Form an equation and find \(x\).

3. Find \(n(A)\), \(n(B)\) and \(n(\xi)\).

4. Find \(n(A'\cup B)\).

5. Explain why \(A\cap B'\) and \(A'\cup B\) together contain every element of \(\xi\), without overlap.