$P$ , $Q$ and $R$ represent switches in 'on' positions and P',Q' and R' represent switches in 'off' positions.Construct a switching circuit representing the polynomial $PR+Q(Q'+R)(P+QR).$Use Boolean algebra to prove that the above circuit can be simplified to an expression in which,when $P$ and $R$ are 'on' or $Q$ and $R$ are 'on',the light is on.Construct an equivalent circuit.