Or versus Not Both: the Birds in the Forest Game Forum

[poirot]

I've been having problems with Preptest 33, Game 2 aka the Birds in the Forest Game. For question 7, In the video on 7sage, it says that according to the "or rule"
for /A -> B , the maximum number of birds in the forest could be 2. This explains why the answer for 7 is E, as both Jays and Shrikes could be in even though the rule is J/ -> S and S/ -> J.

The video goes on to say that for A-> /B, when it says "not both", the maximum number of birds could be 1. I get the latter explanation as to why only 1 of A or B could be in, but I'm terribly confused about the "or rule" mentioned. I assumed that even when it says "not both" that as /A -> B and the contrapositive is B/ -> A, that means that at all time either one is in or out. Why could both A and B be in if the presence of one triggers the other to be out?

If A-> /B did not explicitly say "not both", does this mean that both A and B could also be in? Why does putting the negative in the sufficient rather than the negative completely change the maximum number of birds that could be in the forest?

[papercut]

Or is another way of saying "at least one." You have to have at least one of A and B.

Not both is another way of saying "at most one." You can have at most one of A and B.

So, if you can have at least one of my 2 pencils, can you help yourself to both? Yup.

If you can have at most one of my 2 pencils, can you help yourself to both? Nope.

Not-A --> B
Not-B --> A
Reads: if you don't have one, you must have the other.
Notice how we have no rule above that tells us what to do if we do have A, or if we do have B. Since there's no such rule, we can do whatever we want in either of those two cases with the other "bird."


A --> Not-B
B --> Not-A
Reads: if you have one, you can't have the other. So, you can't have both.

Notice how we have no rule that tells us what to do if we don't have A, or if we don't have B. So, in either of those two cases we can do whatever we want with the other "bird."

[poirot]

Thanks a lot, Papercut! The pencil analogy was really helpful for the or and not both comparison.

As a follow up question, for the problem, when I'm visualizing the In and Out T chart and thinking that it's possible for both A and B to be in the forest when the scenario is
Not A -> B
Not B -> A

would it be fine to visualize the options as A/B within the IN section and then B/A as a floater that could move between the IN and Out categories?

Thank you!

[papercut]

Yup. In the context of an In and Out game, "or" means "at least one is in."

"Not both" means "at least one is out."

So with "or" you save a spot in the in group:
In: A/B
Out:

and with "not both" you save a spot in the out group:
In:
Out: A/B

[poirot]

Great, thank you a ton