Consider the following two statements:

The book is either at Annas house or at Marys house.

Assume A means the book is at Annas house and M means the book is at Marys house. We can represent this as A V M.

We also know that the book cant be at both places at the same time, i.e.

(A & M) V (A & M).

If the book is not at Annas house, then it must be at Marys house, i.e.

A --> M

Given these three statements above, can we determine where the book is?

Explain your answer in detail step by step. You must prove your yes/no answer.