General Question about Rules

[Jkjones3789]

I have a question about two rules of a game I was doing that kind of confused me ...

If yews are not in the park, then either laurels or oaks (but not both are in the park)
SO that means if -Y L or O not both ok ... so then that means if I dont have Y I must have L or O....

This other rule is confusing me and I don't know why ... If it is not the came that the park contains both L and O then it contains both F and S so -L and O F and S and contrapositive -F or S L or O ... Now I know how to write them out but I have no idea what they mean .... If I have F but no S can I still have L or O or L and O its just really confusing me .. please explain to me the implications of this rule. I thought I understood it until I got 3 questions wrong while timing myself .. Thanks so much!

[Adam Tyson]

I'm sure I have seen that game before, but right now can't place it, so I will answer based solely on your description of the rules.

Focusing on the second rule you mentioned, I think you may have mis-diagrammed. If the park doesn't have BOTH L and O then it must have both F and S. That would look like this:

L or O --> F and S

Contrapositive of that rule is:

F or S --> L and O

Saying "if not both" in that rule means that at least one is absent - hence "L or O" as the sufficient condition.

Try that and see if it clears things up?

[Jkjones3789]

Hello, that is actually how I diagrammed it. But I'm still confused I know that we must have Yews or L/O. But with the other rule in consideration are you going to have to F and S or do you need to not have both L and O to have F and S?

These are my rules so you can see the game a little better

A park contains at most five of seven kinds of trees - firs, laurels, maples, oaks, pines and spruces consistent with the following conditions.

If maples are in the park , yews are not.
If firs are in the park, pines are not.
If yews are not in the park, then either laurels or oaks but not both are in the park.
If it is not the case that the park contains both laurels and oaks, then it contains firs and spruces.

I'm getting confused with what I could infer from the rules. I took some contrapositives but what about linkage? Conditional chains? The fact that I must have Y or L/O is really confusing me for some reason ... I'm used to just dealing with one or the other between two not one or the other between 3! lol ... Thanks

[Adam Tyson]

Yes indeed, that link between Y and L/O is an added wrinkle. If you have seen the famous Fruit Stand game, there is a similar rule about K and T, but only those two variables and not a third.

I would start by making a chain and asking myself at each link the question "what else happens?" For example, let's say I do not have Y. Now what? Well, I could have L in and O out. What happens next? With O out, F and S must both be in, right? So what happens next? With F in, P is out. The just leaves one unknown variable - M, which in this case could be in or could be out.

Do the same thing with Y out and O in, and then try Y in. Games like this are sort of like a connect-the-dots puzzle - just follow along and keep making connections. Give it a shot and see what happens!