game simple question!

mc_meatt

Hi, I'm a bit confused with the rule "M and N cannot be selected together."

Is this a biconditional with never together always apart? so, M <--> ~N
Or do I use 'cannot' and think of it as group 4? so, M --> ~N

Which one would be correct?
Thanks for the help.

Micaela_OVO

Not both rule! They could both be out, but both of them can't be in.

M ----> ~N

mc_meatt

@Micaela_OVO
Thanks, if I add the word 'always' to that rule (M and N cannot always be selected together), would that turn this not both rule into a biconditional (always apart, never together)?

quinnxzhang

@"mc_meatt" said:
Thanks, if I add the word 'always' to that rule (M and N cannot always be selected together), would that turn this not both rule into a biconditional (always apart, never together)?

It's still not a biconditional. M <--> ~N means one (and only one) of M and N must be selected. But the "can't be selected together" rule just means that they can't both be selected, not that one must be selected.

If the conditional is confusing, think of the "not both" rule as a "~M or ~N" rule. It's possible that neither is selected, but if one is selected, the other isn't. In your in/out diagram, stick a "M/N" into the out group and don't place anything in the in group.

Micaela_OVO

@mc_meatt I haven't seen that wording on the LG section. It leaves room for confusion.

Some examples of what a bi-conditional rule would look like:
- "M is in if and only if N is in" M <--> N, ~M <--> ~N
- "N is in if M is in, but not otherwise" M <--> N, ~M <--> ~N

- "Either M or N is in, but not both" M <--> ~N

The LSAC will be clear which worlds are possible. Hope that helps!

mc_meatt

@quinnxzhang Thank you thank you~ I think I almost get it except... what would then "always apart, never together' rule look like? I know that 'if and/but only if' is one indicator that indicates this biconditional, but are there any other? or is this 'if and/but only if' pretty much the only one?

@Micaela_OVO Thanks it helped a lot!

quinnxzhang

@"mc_meatt" said:
what would then "always apart, never together' rule look like?

It depends on what you mean by "always apart, never together". For a standard in/out game, if you mean "M and N are never selected together", then this wouldn't be any different than the "~M or ~N" rule. For a grouping game where every piece belongs to a group, "M and N are never together" just means M and N don't belong in the same group.

I suspect that you might be thinking of a grouping game with two groups. If every piece must be grouped into one of the two groups, then I suppose you could represent your rule as a biconditional. Something like "M1 <-> ~N1", where "~N1" is equivalent to "N2". But this only happens in this restricted case, and most of the time "not together" is not a biconditional.

Cant Get Right

I'm not sure how "always" would work here. That says to me, they can be selected together, just not for every board. I'm not sure how that would work. Maybe for a pattern game.

To make this a biconditional in a standard in/out game, you'd have to have something that told you that one of them had to be in. There's a number of ways they could do that. Maybe an additional rule, or maybe they extend this rule to say but one of them must be selected or something.

The way the question is worded, it's clear that this is from an in/out game, but for certain incarnations of grouping games, I think this can serve as a never together always apart rule. Groups in an in/out game have qualities which regular grouping games do not necessarily have. So in your example, by saying they can't be "selected," it is effectively specifying that they cannot both be chosen for the in group. So in a grouping game we could see this rule in two ways. If it's a 1 to 1 table game or something and it said, M and N cannot be seated at the same table, they would be forever apart in that situation. We could also replicate the in/out version by specifying a specific group to which the rule applies. "M and N cannot both be seated at table 1" would not imply never together. There is nothing stopping them from being together at table 2.

The point here is that the context of the rule matters. You should always interpret this as a group 4 translation, and anything beyond that (like the never together situation in the table game) is more of an inference.