Answer to Question #259422 in Discrete Mathematics for King

Question

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) ∃S(x, open)

(b) ∀x(S(x, malfunctioning) ∨ S(x, diagnostic))

(c) ∃xS(x, open) ∨ ∃xS(x, diagnostic)

1

Answer 1

Let us 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) It follows that the specification $∃S(x, open)$ into English is "There exists $x$ that is in state $open$".

(b) It follows that the specification $∀x(S(x, malfunctioning) ∨ S(x, diagnostic))$ into English is "Any state $x$ is $malfunctioning\ or\ diagnostic$".

(c) It follows that the specification $∃xS(x, open) ∨ ∃xS(x, diagnostic)$ into English is "There exists $x$ that is in state $open$ or there exists $x$ that is in state $diagnostic$".