Chapter 1.4, Problem 41E

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

41. Translate these specifications into English, whereF(p) is "Printerpis out of service,”B(p) is “Printerpis busy,”L(j) jobjis lost," andQ(j) is "Print job j is queued."

a) $\exists p\left(F\left(p\right)\wedge B\left(p\right)\right)\to \exists jL\left(j\right)$

b) $\forall pB\left(p\right)\to \exists jQ\left(j\right)$

c) $\exists j\left(Q\left(j\right)\wedge L\left(j\right)\right)\to \exists pF\left(p\right)$

d) $\left(\forall pB\left(p\right)\wedge \forall jQ\left(j\right)\right)\to \exists jL\left(j\right)$