In/Out Game with Multiple Necessary Conditions on Tail of Chain

NorthSide60660

Consider this chain:

A —> B—> /C or /D

I understand Demorgan's Law Regarding Contrapositives. But how do we work with the 'possible worlds' this chain represents?, particularly w/r/t moving backwards along this chain.

I believe it means 'If B, then "C not D, or D not C, or Not C not D.'. If that's correct, my next question is what would require triggering the negation of B?

If I'm presented in an AC with "Assume D", can I negate B?

In my mind, negating B requires BOTH Not C and Not D. Is that incorrect?

Also, what can I count on, if I have B? In out questions require us to move forward and backwards on these chains. It can get confusing. I would think, if B, I can't count on anything specific, because we could have not C or not D or neither. Or it appears I can count on NOT BOTH C and D.

Thank you.

NorthSide60660

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Cant Get Right

Looks like you've got it. It does take both C and D to trigger the contrapositive, and when you have B, you don't know which of /C or /D or both you might have.

Depending on what all else is going on, I'd probably want to split on B and be done with it:

Where B is in, A is a floater and you enter in a C/D item in the out group and create the D/C floater item.
Where B is out, A is out and C and D float freely.

With the split, you incorporate all that complexity on the board instead of having to apply it throughout the game. You do it once upfront and then you never have to think about it again.