Undergraduate degree Required for appointment to the executive board.
If felony conviction, then no appointment.
Conclusion: Murray cannot be accepted for the position of Executive Administrator, since he has a felony conviction.(even though his is undergraduate).
Pre Thinking: Appointment to board is the only way for the position of Executive Administrator.
a. Anyone with a master's degree and without a felony conviction is eligible for appointment to the executive board.
--> TRAP, Don't assume he must be undergraduate. We don't know. b. Only candidates eligible for appointment to the executive board can be accepted for the position of Executive Administrator. -->
As per our pre thinking.c. An undergraduate degree is not necessary for acceptance for the position of Executive Administrator. -->
It is necessary, man.d. If Murray did not have a felony conviction, he would be accepted for the position of Executive Administrator. -->
ACCEPTED is the problem here. Getting a chance for appointment doesn't mean he would be accepted. I have my interview appointment with Google. But does that mean I would be accepted? I wish I were. 
e. The felony charge on which Murray was convicted is relevant to the duties of the position of Executive Administrator -->
Really? How do we know?