Chapter 1.4, Problem 40E

Exercises 40-44 deal the translation between system specification and logical expressions involving quantifiers.

40. Translate these system specifications into English, and where the domain forxandyconsists of all systems and all possible states, respectively.

a) $\exists xS\left(x,\text{open}\right)$

b) $\forall x\left(S\left(x,\text{malfunctioning}\right)\vee S\left(x,\text{diagnostic}\right)\right)$

c) $\exists xS\left(x,\text{open}\right)\vee \exists xS\left(x,\text{diagnostic}\right)$

d)

   $\exists x\neg S\left(x,\text{available}\right)$

e) $\forall x\neg S\left(x,\text{working}\right)$