Hi, I would start by figuring out what must be true if L and Q are in
In: L Q Out:
We know j must be out according to the second rule, and according to the fourth rule, we know that s must be in
In: L Q S Out: J
This forces M out according to the final rule, which in turn forces F out according to the first rule.
In: L Q S Out: J M F
This leaves only p as the last once we have not determined yet. However, since we can use this to show that a through d cannot happen, and we know e can happen, E is correct.