It does not work, and here is my long-winded explanation of why! Based on your comment, I am assuming you used that statement as a contrapositive of a statement like "If you have C, then you have A and B". C → A and B

Your version of the contrapositive says "If you don't have A and you don't have B, then you don't have C." /A and /B → /C

But what if you have A but no B? Or what if you don't have A but you do have B? This statement does not answer those questions and instead prompts you to make unwarranted assumptions in a way the original statement does not, and therefore it is not logically equivalent to the original statement.

The correct contrapositive would be "If you don't have A or you don't have B, then you don't have C." /A or /B → /C

This way, you capture what happens if you have neither A nor B, if you have just A but no B, and if you have just B and no A. I think the key here is remembering that the "or" is inclusive, it can do more than "and" because it can insinuate one, or the other, or both, while "and" just means both. That is why you can't keep "and" or "or" the same when creating the contrapositive statement, they have different meanings.

Since I could've been wrong in guessing what the original statement was that you provided the contrapositive too, I will also provide an example working backwards from your version of the contrapositive. "If you don't have A and you don't have B, then you don't have C." /A and /B → /C.

This cannot be flipped to C → A and B because in plain english that means "If you have C, then you have both A and B." Well, we don't know if we need both A and B to have C in the original statement. We just know that if you do not have both A and B, then you do not have C. But that could still mean that you can have C with just A or just B.

The correct contrapositive would be C → A or B, "If you have C, then you have A or you have B (or you have both).

I know this was posted a little while ago and you may have figured it out, but I wanted to test my own brain a bit and maybe help anyone else that has the same question :)

The way I understand it is "or" on the LSAT is always inclusive. "And" means both, while "or" can mean one or the other, or both.

Your translation is correct, M -> N and O means "If M is adopted, then both N and O are adopted." An easier way to say this is that M requires both N and O.

This is logically equivalent to to the original statement, /N or /O -> /M, "If either N or O (or both) are not adopted, then M is not adopted." Because M requires both N and O, if either one is not adopted, then M will not be adopted.