QUESTION: Given the sentence "A woman holds a drink while a man and a woman examine a book." is it true that "A woman is driving a car while a man and a woman sit in the back."?

Let's solve it slowly: A woman would not hold a drink while she is driving (hopefully).
The answer is no.

QUESTION: Premise: "A black dog runs through a field."
Hypothesis: "A black dog is laying in the field."
Do we know that the hypothesis entailed by the premise?

Let's solve it slowly: A dog can not be laying down and run at the same time.
The answer is no.

QUESTION: Given the sentence "This young girl is wearing a red and black checkered shirt." is it true that "The shirt is made of cotton."?

Let's solve it slowly:
This young girl is wearing a red and black checkered shirt does not indicate that the shirt is made of cotton.
The answer is it is not possible to tell.