Chapter 1.3, Problem 51E

We now present a group of exercises that involve the logical operators NAND and NOR. The propositionpNANDq, is true when eitherporq, or both, are false; and it is false when bothpandqare true. The propositionpNORqis true when bothpandqare false, and it is false otherwise. The propositionspNANDqandpNORqare denoted by $p|q$

$p\downarrow q$, respectively. (The operators |and $\downarrow$are called theSheffer strokeand thePeirce arrowafter H. M. Sheffer and C. S. Peirce, respectively.)

51. Show that $p|q$is logically equivalent to $\neg \left(p\wedge q\right)$.