Inferences from Bi-conditionals?

yellowavcable

Is it possible to chain up bi-conditionals, and if so, what inferences can be drawn? For instance, imagine a a grouping game with three groups and the following rules:

A and B are not in the same group.
B and C are not in the same group.

The rules are:
A <---> B
B <---> C

If we take the contrapositive of the second rule (C <---> B), I believe we can link them up. A <---> B <---> C.

Can we conclude A <---> C? But if the game includes three groups, then does this inference even matter?

Cant Get Right

@yellowavcable said:
Can we conclude A <---> C? But if the game includes three groups, then does this inference even matter?

This is a really important distinction, and it's why we should not represent these rules using biconditionals. For an in/out game, it would work, but you still don't want to be in the habit of doing this. In this situation it would only work because of the nature of in/out games, not because it's correct. Instead of biconditionals, these should be represented with standard "not both" conditionals:

A --> /B
B --> /C

So with common terms, we can always combine our rules. But here it would be:

A or C --> /B

yellowavcable

I see, very helpful—thanks!