Translate each of these English statements into logical expressions using predicates, quantifiers, and logical connectives. Use the same domain of discourse for both statements, and explicitly state what that domain is. (a) All tools are in the correct place and are in excellent condition. (b) Everything is in the correct place and in excellent condition. Translate these system specifications into English. The predicate S(x, y) means "x is in state y". The domain for x is all systems. The domain for y is all possible states. (a) exist x S(x, open) (b) Forall x (S(x, malfunctioning) S(x, diagnostic)) (c) exist x S(x, open) exist x S(x, diagnostic) (d) 3x S(x, available) (e) Forall x S(x, working) Express each of these system specifications using predicates, quantifiers, and logical connectives. Explicitly state what each of your predicates are, and what the domain of discourse is for each variable. You may use different predicates and domains for each of the statements. (a) Every user has access to an electronic mailbox. (b) The system mailbox can be accessed by everyone in the group if the file system is locked