For each of the following english statements, (i) translate it into predicate logic, (i) write the negation of that statement in predicate logic with the negation symbols pushed as far in as possible so that any negation symbols are directly in front of a predicate, and then (ii) translate the result of (ii) back to english (natural if possible). for the logic, let your domain of discourse be cats and activities. you should use only the predicates loves(z, y) and likes(x, y) which say that cat z loves or likes (respectively) activity y: the predicates cat() and which say whether x is a cat or activity (respectively); and the predicates x -y and z ^y, which say whether and y are the same object.

(a) 6 points] sleeping is the only activity that garfield likes.

(b) [6 points] there is an activity that is loved by some cat but liked by all cats.

(c) [6 points] cats that love sleeping don't like some activity.