Let's parse through this again for clarity:

Premise: "If taught with appropriate methods & devote effort, then broad mastery."

P1: TMA & DE BM

P1': BM TMA OR DE

Conclusion: "If no broad mastery, then no taught with appropriate methods."

C: BM TMA

C': TMA BM

Now, remember the task for Justify the Conclusion problems. You must start on the left (sufficient) side of the conclusion. The goal is to take the information in the stimulus and combine it with one of the answer choices to demonstrate that the sufficient side of the conclusion implies the posited necessary outcome.

In other words, you should:

- Assess the left side of the conditional in the conclusion to see what the purported sufficient condition is.
- See what information we have so far in the premises to see how far that will get us.
- Notice what is missing. What would combine with the premises to show that the left side of the conditional in the conclusion always implies the right side?
- Look in the answer choices to find the answer that fills in this gap.

- Either we need to show that BM is sufficient for TMA OR we need to show that TMA is sufficient for BM (this is because the conditional and its contrapositive are equivalent). For simplicity sake, let's just pick one. We're going to try to show that BM is sufficient for TMA.
- What do the premises tell us with respect to BM? From P1' (the contrapositive of the premise), we see that BM TMA OR DE. In other words BM gets us to either TMA OR DE or both.
- Well, that's not good enough. We need BM to get us to TMA. We need it to obviate (make unimportant) DE. Now your prediction comes in. How could we do this? How could we show that BM TMA all by itself without DE? Well, there are a couple ways. We could show that BM TMA AND DE (in other words, just spell this out) or we would have to find a way to show that DE TMA. Why does this work? Because it shows that you can't have DE without TMA. Thus either we would have (BM with TMA & DE) OR we would have (BM with TMA & DE). Either way we would show that BM TMA.

To illustrate, since Answer Choice (A) is the correct answer, we want to end up showing that DE TMA does the job when combined with P1' BM TMA OR DE. Before we get there, let's consider all the possibilities.

Remember that our job is to start on the sufficient side of the conclusion (BM TMA) and end up on the necessary side. So where do we begin? Assume:

- BM (the sufficient side of the conclusion). Take that and apply it to P1' BM TMA OR DE:

BM right now implies that we have 1 of 3 possibilities:

1) TMA & DE

2) TMA & DE

3) TMA & DE

With respect to the conclusion, which of these options from the premise works? Only options 2 and 3. Option 1 doesn't work. Now go back to our two possible answer choices that would get us to this outcome:

- i) BM TMA & DE

- ii) DE TMA

- 1) TMA & DE. Does this work with DE TMA? No, this creates a contradiction. If you have DE, then you must have TMA.

2) TMA & DE. Does this work with DE TMA? Sure, DE is sufficient for TMA but is not necessary for TMA

3) TMA & DE. Does this work with DE TMA? Sure. All good. DE TMA so DE & TMA is fine.

I know this is a lot, but I wanted to give you an in-depth explanation. For simplicity sake, just follow the rules I outlined above. Make sure that you have your information diagrammed correctly. Then follow the process step-by-step with the answer choices until you find the one that meets your criteria. I know you can do this!