Assuming the statements "If Alice owns a cat, she doesn't own a dog".

Would the following translation be fine?

```
O(A,C) IMPLY NOT O(A,D)

```

Where O(X,Y) implies X owns Y, A = Alice, C = Cat, D = Dog?

The answer from the book wants the predicates to be A(X), C(X), D(X), and the statement to begin with "For all X such that O(A(X), C(X)"... But I'm not sure about this. Alice is one person, so the phrase "For all X such that X is Alice" wouldn't make much sense, wouldn't it be possible to define Alice as "A"?