An undergraduate degree is necessary for appointment to the executive board.
Evidence (since)
No one with a felony FC → ~EB conviction can be appointed to the [executive] board.
Murray has a felony Murray is FC conviction.
Conclusion (thus)
Murray cannot be Murray is ~EA accepted for the position of Executive Administrator.
Evaluate
We can see that the claim we're trying to prove has a New Concept, "Executive Administrator". The argument must be assuming something about EA, so we can trash any answer that doesn't talk about EA.
Given what we were told, since Murray has a felony, he can't be appointed to the board. The conclusion is trying to get from that negative idea to the negative idea that he can't be Executive Administrator.
Goal
So the author must be assuming, or by contrapositive
~AB → ~EA or EA → AB