For each of the following English statements, (i) translate it into predicate logic, (ii) write the negation of that statement in predicate logic

For each of the following English statements, (i) translate it into predicate logic, (ii) 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 (iii) translate the result of (ii) back to (natural) English.

For the logic, let the domain of discourse be cats and food. Use only the predicates Loves(x, y) and Likes(x, y) which say that cat x loves or likes (respectively) food y; the predicates Cat(x) and Food(x), which say whether x is a cat or food (respectively); and the predicates x = y and x 6= y, which say whether x and y are the same object. (Use the constant "Garfield" to refer to Garfield in your logical statements.)

(a) If a cat loves fish and lasagna, then it's Garfield.

(b) There is some food that Garfield likes but no other cat likes.

(c) Every cat likes some food that Garfield does not like.