Chapter 1.3, Problem 61E

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.)

61. The following sentence is taken from the specification of a telephone system: "If the directory database is opened, then the monitor is put in a closed state, if the system not in its initial state," This specification is hard to understand because it involves two conditional statements. Find an equivalent, easier-to-understand specification that involves disjunctions and negations but not conditional statements.