Can't prove the sufficient

Hi @KimJongUn, thanks for your post, but we are not entirely sure we understand your question. You cannot take a necessary condition and assume that the sufficient exists; this is a logical fallacy known as an incorrect reversal. Without committing this logical fallacy, you can reach the correct answer. You are told on Question 2 that the program offers Literature (L). OK, so what else do we know? (A) can be eliminated by combining the positive of the second rule (L ==> G and not P) and the contrapositive of the third rule (not P or Z ==> not S). Thus: if L ==> not P ==> not S. So Sociology cannot be offered. (B) can be eliminated by combining the positive of the second rule (L ==> G and not P) and the positive of the fourth rule (G ==> H and Z). Thus: if L ==> G ==> H. Which means if Literature is offered, then History must also be offered. So it cannot be true that History is not offered. (C) is the correct answer. Why? It could be true that Mathematics is offered. The first rule tells us that if Mathematics is offered, then either Literature or Sociology - but not both - is offered. This rule can be diagrammed as two separate positives. First: M ==> L or S. Contrapositive: not L and not S ==> not M. Second: M ==> not L or not S. Contrapositive: L and S ==> not M. Notice that these diagrams of the first rule are consistent with a universe (like this fact pattern) where L is offered and M is offered. (D) cannot be true. As explained above (with respect to answer (B)), if L ==> G ==> H and Z. That's at least 4 courses that have to be offered because of L being offered. (E) cannot be true, either. L==>G==>H and Z. So Z must be offered. Hope that helps! Please let us know if you have any additional questions.