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The game is about a park that contains seven kinds of trees. It destroyed me during a PT, probably one of the harder in and out games I've encountered in some time.

I know where I went wrong and I'm trying to wrap my head around a couple rules, because I've never diagrammed or interpreted a rule in these ways.

If yews are not in the park, then either laurels or oaks, but not both, are in the park.

In a test I would intuitively diagram the rule like Not Y > L or O (not both) .... and then move on
But apparently, in addition to this rule you're suppose to also diagram it like this... Not Y > Not L and Not O?

I understand the significance of this rule, if Y is selected, it can't be the case that L or O are both not selected. However, it just seems really counter intuitive, since it technically doesn't speak to a logical consequence? Am I right? Does anyone mind simplifying this for me? The reason I'm worried is because if you didn't quickly diagram the rule in these two ways, then you pretty much got slaughtered on the game.

I'm just working from your post, since I haven't seen the particular LG in question, but the second rule you gave (Not Y > Not L and Not O) doesn't seem to be correct, since that's saying that if yews are not in the park, then both laurels AND oaks must be absent as well, which contradicts the problem statement "If yews are not in the park, then either laurels or oaks, but not both, are in the park."

I would have just gone with NOT Y > L XOR O, where "XOR" is "Exclusive OR", meaning "one or the other, but not both".

You can think of it as two statements:

~Y --> L or O
~Y --> ~(L & O)

There are other ways to do it, but the only really tricky thing is that there are two ways to invoke the contrapositive for this rule: having neither L nor O, or having both L and O. Several times in the game you need to be able to realize that once you have L and O, Y must also be in the park.