Chapter 1.3, Problem 58E

We now present a group of exercises that involve the logical operatorsNANDandNOR. The propositionp NAND q, is true when eitherporq, or both, are false; and it is false when bothpandqare true. The propositionp NOR qis true when bothpandqare false, and it is false otherwise. The propositionsp NAND qandp NOR qare 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.)

58. Show that $p|\left(q|r\right)$and $\left(p|q\right)|r$are not equivalent, so that the logical operator $|$is not associative.