When is a necessary assumption of an argument...

[mitchliao]

When is a necessary assumption of an argument a sufficient necessary statement?

I imagine if the argument was...

Premise 1: A
Conclusion: B

Then, the necessary assumption would have to be... If A then B.

Well, I was wondering in what other cases that people have encountered or ones that you can just think up off the top of your head, when the question stem asked something to the effect of "which one of the following answer choices is a necessary assumption for the argument above?"... the right answer choice was a sufficient necessary statement.

Thanks

[ManhattanPrepLSAT1]

Glad that you noticed that! Usually the correct answer to a Necessary Assumption question will not be sufficient, but you're correct in that sometimes they are. You're example does a nice job of reflecting the circumstances around the majority of the instances where the answer choice is both sufficient and necessary. Typically this occurs when the question is testing conditional logic. Most Necessary Assumptions don't test conditional logic - this is typically saved for Sufficient Assumptions. But some Necessary Assumptions do test it and for them, the answer choice is frequently both Necessary and Sufficient. Check out the following examples if you'd like to see a few more of these:

PT23, S2, Q9
PT27, S4, Q20
PT31, S3, Q11

Good luck!

[chike_eze]

Glad that you noticed that! Usually the correct answer to a Necessary Assumption question will not be sufficient, but you're correct in that sometimes they are...

The way I've been thinking about it is thus:

If A then B:
A is sufficient evidence for necessary conclusion B
But A is not necessary evidence to conclude B

If A then B and only if:
A is sufficient and necessary evidence for necessary conclusion B. And B is sufficient and necessary evidence for conclusion A

Is this reasoning valid? Please explain.

[ManhattanPrepLSAT1]

Absolutely! Let's put it to the test...

If it rains, you get wet.

Given that it rains, can you conclude that you'd get wet? Sure!

Given that your wet, can you conclude that it had rained? Nope. Maybe you just got hit with the water hose.

What about the following though.

Brian will wake up if, but only if, you make him coffee.

Now both of those events are mutually dependent. Either you'll make him coffee and he'll wake up, or you won't make him coffee and he won't wake up. But it's not possible for one to conclude that he'd wake up without coffee or that you'd make him coffee with him waking up.

Thanks for posting your example. I personally enjoy the fact that I get to play with conditional logic all day for work!

[matt.sim]

This is exactly what I was looking for. Just to confirm if I understand the question correctly, could you verify if my logic is correct?

Premise: A -> B
Conclusion: A -> C

Necessary Assumption B -> C
Sufficient Assumption B -> C

Thanks in advance.