You're asking to put a list of responsibilities. Then, asking if the question is true or false. Please clarify. And also, responsibilities as a parent would fall into the "Home-Ec" category. Not Health. However, I will answer your question.
Feeding, providing liquids, keeping the child from dying, providing a place to sleep, nurturing, (this is more of a mother thing) singing a lullaby to help the child sleep or when the child is upset. There are a few I don't know about, but when I become a parent, I'll know.