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 system and all possible states, respectively.
- $\exists x S(x, open)$
- $\forall x S(x, malfunctioning ) \vee S(x, diagnostic)$
- $\exists x S(x, open ) \vee \exists x S(x, diagnostic)$
- $\exists x \sim S(x, available )$
- $\forall x \sim S(x, working)$