Question #190955

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)


1
Expert's answer
2021-05-10T13:09:22-0400

Given,

S(x,y)="x is in state y"S(x,y)="\text{x is in state y}"


Negation ¬p: not p\lnot p:\ not\ p

Disjunction pq:p or qp\lor q: p\ or\ q

Existential quantification xP(x):\exists xP(x): There exists an element x in domain such that P(x)

Universal quantification  xP(x):P(x)\forall\ xP(x):P(x) 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.

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