Answer
This exercise is similar to Exercise 50.
Work Step by Step
First, we can see from the truth tables that (p|p)≡(¬p) and that ((p|p)|(q|q))≡(p∨q). Then we argue exactly as in part(c) of Exercise50: by Exercise45, every compound proposition is logically equivalent to one that uses only ¬ and ∨. But by our observations at the beginning of the present exercise, we can get rid of all the negations and disjunctions by using Nands. Thus every compound proposition can be converted into a logically equivalent compound proposition involving only NAND’s.
