The game requires us to select four out of six potential nominees - F G H J K L -for four positions: 1 M, 1 T, and 2 C. The question asks us which of the following must be true if G is a nominee for C.

We can infer that if G is a nominee, F is not a nominee per rule (1):

If F is a nominee, then G is not a nominee, we can infer from that rule that: If G is a nominee, then F is not a nominee.

We can then infer that is F is not a nominee, H must be a nominee for treasurer per rule (3):

Either F or H must be a nominee for treasurer. F is not a nominee. H must be a nominee for T.

Therefore, we can conclude that (E) must be true.

Let me know if this makes sense and if you have any further questions.