Chapter 6.2, Problem 25E

To determine

To prove: For the sets S, A and B, $n\left({\left(A\cap B\right)}^{\prime }\right)=n\left(A^{\prime }\right)+n\left(B^{\prime }\right)-n\left({\left(A\cup B\right)}^{\prime }\right)$.

If, $S=\left\{\begin{array}{l}\text{Barnsley, Manchester United, Southend, Sheffield United, Liverpool,}\\ \text{Maroka Swallows, Witbank Aces, Royal Tigers, Dundee United, Lyon}\end{array}\right\}$,

$A=\left\{\text{Southend, Liverpool, Maroka Swallows, Royal Tigers}\right\}$ and

$B=\left\{\text{Barnsley, Manchester United, Southend}\right\}$.