Translate these system specifications into English where the predicate S(x, y) is “x is in state y” and where the domain for x and y consists of all systems and all possible states, respectively. a) ∃xS(x, open) b) ∀x(S(x, malfunctioning) ∨ S(x, diagnostic)) c) ∃xS(x, open) ∨ ∃xS(x, diagnostic) d) ∃x¬S(x, available) e) ∀x¬S(x, working)
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Existential quantification There exists an element x in domain such that P(x)
Universal quantification for all values of x in the domain.
Using the above interpretations, we can translate the prepositions into English.
a) There exists a system that is in the state open.
b) All systems are in the state malfunction or in the state diagnostic.
c) There exists a system that is in the state open or there exists a system that is in the state diagnostic.
d) There exists a system that is not in the state available.
e) All systems are not in the state working.