You are given the predicates Cat(x), which is true if x is a cat, Dog(x), which is true if x is a dog, Good(x), which is true if x is good, Day(x), which is true of x has a day, and Friend(x, y), which is true if x and y are friends. Since your keyboards probably do not have the special logic symbols, use these symbols to write the logic sentences in parts (a) and (b): A means "for all" E means "there exists" & means "and" l means "or" - means "not" --> means "implies"
(a) Translate the following sentence into first-order logic: All dogs like each other. (b) Translate the following sentence into first-order logic: Cats hate everything that dogs like. (All things that are liked by all dogs are hated by all cats.) (c) (10 points) Translate the following sentence from first-order logic into English: 3x Dog(x) ^ [Vy Cat(y) => Likes(x, y)] (d) (10 points) Translate the following sentence from first-order logic into English: Vx By Cat(x) - [Dog(y) 1 Likes(x, y)]