Exactly one of Mr. Jankowski, Mrs. Jankowski, their son Nate, and their daughter Mabel is a butcher.

Five facts relating to their occupation are furnished hereunder as follows:

1. If the butcher and the baker belong to the same sex, then the baker is older than the butcher.
2. There is exactly one butcher and one baker.
3. If neither the butcher nor the baker is the parent of the other, then the butcher is older than the baker.
4. If the butcher is a man, then he and the baker are the same age.
5. If the butcher and the baker belong to the opposite sex, then the man is older than the woman.

Whose occupation can be determined with certainty? Provide valid reasoning for your conclusion.