All pizzas are food. I have not eaten any food today. Have I eaten any pizzas today?
No. You stated you have not eaten any food today, and since all pizzas are food, it can be deduced that you have not eaten any pizzas today.
Correct! Here's another problem:
All red things are apples. I do not own any apples. Do I own any red things?
No, you stated that you do not own any apples and since all red things are apples, it can be deduced that you do not own any red things.