Notice that on inputs $0$ and $1($the binary representations of true and false$)$ the binary and gate gives the minimum of its two inputs a and b: it returns $0$ except in the case a $=$ b $=1.$ Similary, the or gate gives the maximum of its two inputs: it returns $1$ except when a $=$ b $=0.$ Design a sorting circuit with two inputs and two outputs, sorting them into order. Then use that circuit as a $$black box$$ to sort three inputs p$,$ q$,$ r and three outputs p $0,$ q$0,$ r$0,$ where p $0$ q $0$ r $0.$