Let me try this one.
Many students are confused by: 1) How to diagram the answers correctly; 2) What's going on with answer (A) and (D).
1) Diagrams
(A) -EW -> ID or -ID -> EW
(B) UR -> PRC
(C) EW -> ID
(D) -EW -> PRC or -PRC -> EW
(E) -UR -> -EW or EW -> UR
2) Choose (A) or (D)
What the stimulus told us:
1. EW -> PRC
EW -> UR -> ID
and don't forget we're also told:
2. -ID
from which we can infer:
-ID -> -UR ->-EW
This is the key to deciding whether answer choice (A) or (D) is the correct must be false answer.
Les't talk about answer (A) and (D):
(A) -EW -> ID or -ID -> EW
The first part -EW -> ID could be true at first. It is consistent with EW -> UR -> ID. We only know that when the economy is weak, investment decreases. But we don't know what if economy is not weak. So, they are consistent with each other. There is no violation.
Except that we are told -ID is true now. The first part tells us ID is true. They are in conflict. So the first part cannot be true.
The second part -ID -> EW cannot be true. Because we are told in the stimulus that EW -> UR -> ID. Taking contrapositive of this, we know -ID -> -UR -> -EW. That is -ID -> -EW, which contradict the second part -ID -> EW.
Now, both parts of answer choice (A) cannot be true. It's the correct answer.
(D) -EW -> PRC or -PRC -> EW
The first part -EW -> PRC could be true. It is consistent with EW -> PRC. We only know that when the economy is weak, prices remain constant. But we don't know what if economy is not weak. So, they are consistent with each other.
The second part -PRC -> EW cannot be true. Because we are told in the stimulus that EW -> PRC. Taking contrapositive of this, we know -PRC -> -EW, which contradict the second part -PRC -> EW.
Which one should we choose? We are given -ID, which carries -ID -> -UR -> -EW with it. So, we can infer three facts given: -ID, -UR and -EW. Now it's clear, we should accept -EW as the sufficient condition, which means we should choose the first part. Because we are never told that -PRC is true, we don't know if the second part should apply. So, answer (D) could be true.
Or, you can think it in this way: Although the second part cannot be true, but the first could still work. It is not totally false. Under some circumstance (when -EW is true), it could be true. So, we cannot say answer choice (D) is definitely false.
Answer choice (A) is the right answer.
Hope this helps. Good luck on LSAT.