Chapter 1.3, Problem 62E

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.)

62. How many of the disjunctions $p\vee \neg q,\neg p\vee q,q\vee r,q\vee \neg r$,

$\neg q\vee \neg r$and can be made simultaneously true by an assignment of truth valuestop,q, andr?