You have left something out.
M -> B | ~M & ~B
Doesn't necessarily follow. If you have not B, then you can infer not M by Modus Tollens, but as it stands the conclusion is invalid.
In other words, the problem would have to read: "If the murder happened in the hotel room, then there are bloodstains somewhere in the room. There are no bloodstains in the room. It follows that it is not the case that the murder happened in the hotel room and there are not bloodstains somewhere in the room." Then your proof would look like:
1. M -> B 2. ~B | ~M & ~B 3. ~M 1, 2 Modus Tollens 4. :. ~M & ~B 2, 3 Conjuction Introduction
John
My calculator said it, I believe it, that settles it
