The Sheffer stroke is a connective denoted | and defined by the following truth table:...

The Sheffer stroke is a connective denoted | and defined by the following truth table:

The following parts prove that all of the basic connectives can be written by using only the Sheffer stroke:

(a) Show that p|p is logically equivalent to ~p.

(b) Show that (p|p)|(q|q) is logically equivalent to .

(c) Show that (p|q)|(p|q) is logically equivalent to .

(d) Show that p|(q|q) is logically equivalent to p →q.