Sets

Consider the claim
\[A\cup B'=A\cap B'.\]

1. Give an example of sets \(A\) and \(B\), within a stated non-empty universe, for which the claim is false.

2. Determine the exact relationship between \(A\) and \(B'\) that makes the equality true.

3. Justify your answer to part (b).

4. Express this relationship using \(A'\) and \(B\).