Whenever she considers voting in an election to select one candidate for a position and there is at least one issue important to her, Kay uses the following principle in choosing which course of action to take: it is acceptable for me to vote for a candidate whose opinions differ from mine on at least one issue important to me whenever I disagree with each of the other candidates on even more such issues; it is otherwise unacceptable to vote for that candidate.
Principle
This one is a BEAST to translate. "Whenever" is the conditional key word in the first part of the principle, and that introduces the condition on the left: if Kay disagrees with each of the OTHER candidates on MORE important issues than some particular candidate, then it's acceptable to vote for that particular candidate. So, for example, if Kay disagrees with candidate X about 1 important issue and disagrees with the other candidates Y and Z about 2 important issues, it's acceptable for Kay to vote for candidate X.
The second half of the principle begins after the semicolon: It's otherwise unacceptable to vote for a candidate who disagrees with her on an important issue. This means that if Kay DOESN'T disagree with all the other candidates on more important issues than some particular candidate, then it's NOT acceptable to vote for that candidate. So, in that same example where Kay disagrees with candidate X about 1 important issue and candidates Y and Z about 2 important issues, it's NEVER acceptable for her to vote for Y and Z, even if she likes them better personally, thinks they'd be a better leader, etc.
Facts
There is only one issue important to Kay, and of the three options (L, M, and N), only M share's K's position on that 1 important issue.
Evaluate
Since L and N disagree with Kay's position on the important issue, and since there's no way for them to agree with Kay on other important issues (because there ARE no other important issues to Kay), that means it's unacceptable for K to vote for them.
We don't technically have a way to prove that it's acceptable for Kay to vote for M, because the rule provided for "acceptable" involves a trigger that doesn't apply to M.
The trigger talks about a candidate whose opinions differ on at least one important issue. There's only one important issue to Kay, and M's opinions do not differ. So we can't really apply this rule to M, even though our common sense would tell us it seems acceptable for her to vote for M
Goal
Look for an answer that reflects that it is unacceptable to vote for L and N, that it's potentially acceptable to vote for M, or both.