Looking at both the given premises and their contrapositives, we can use the transitive property to combine the variables into a chain in order to make a conclusion:
C: not B -> A -> not Z -> F not F -> Z -> not A -> B
I assume your question "How do we know that A and B are mutually exclusive?" is referring to answer choices (A) and (B), not the variables A and B from the premises. We don't necessarily need to know that the answer choices are mutually exclusive, we just need to find the one that is directly supported from the given premises. Since there can only be one correct answer, it is safe to assume that the LSAT will not give two answer choices that are both directly supported and answer the question. In this case, option (A)'s conclusion that B -> not F is not supported by the transitive chain we made above, but answer choice (B)'s conclusion that not B -> F is directly supported in the first chain we constructed. Therefore, choice (B) can be properly concluded from the given premises and choice (A) cannot, so it does not matter if they are mutually exclusive.
If you are asking about the variables A and B instead of the answer choices (A) and (B), please note that they are not mutually exclusive. We know that there must be at least one variable at play, but we do not know what will happen if A or B was the Sufficient condition. It could be possible for both variables to coexist. This is similar to how we interpret the "either or" rule in group game setups in the logic games section.
Does this make sense? Please let us know if you have any additional questions.
