Let's look at the first premise, X - - - -> Y. X is the sufficient condition, Y is the necessary condition. We know that if the necessary condition fails, then so does the sufficient condition. X cannot exist without Y. This is how we derive the following contrapositive.
not Y - - - - - > not X
What other premise would lead to the conclusion that X does not exist? This is what answer choice B gives us. Y does not exist. Given this, we can conclude that X does not exist, based on our contrapositive.
