In/Out Grouping Game Question

[hnadgauda]

On page 351 of the LG Strategy Guide, I do not understand why S is sold and R is not. What are we supposed to do with the contradicting rules?

Originally we had "If S is not sold at auction, neither is R":

~S-->~R
R-->S

and now we have "Either R or S is sold, but not both":

R<-->~S
~R<-->S

How do all these rules together result in S is sold and R is not?

[ohthatpatrick]

The rules don’t contradict, but they lead to a certain inference.

The rule that says “Either R or S is sold, but not both”, on its own, creates two possible worlds
IN: R
OUT: S

or

IN: S
OUT: R

But when we consider the rules of the game, we know that “If S is OUT, R is OUT”

So clearly that 1st world is not possible under the rules of the game.

Thus, we know that the 2nd world must be what’s going on for Q4.

IN: S
OUT: R

This complies with the rule that says ‘If S is out, R is out”
and it complies with the rule that says ‘Either R or S, but not both, is IN”

[hnadgauda]

The rules don’t contradict, but they lead to a certain inference.

The rule that says “Either R or S is sold, but not both”, on its own, creates two possible worlds
IN: R
OUT: S

or

IN: S
OUT: R

But when we consider the rules of the game, we know that “If S is OUT, R is OUT”

So clearly that 1st world is not possible under the rules of the game.

Thus, we know that the 2nd world must be what’s going on for Q4.

IN: S
OUT: R

This complies with the rule that says ‘If S is out, R is out”
and it complies with the rule that says ‘Either R or S, but not both, is IN”

Thank you! I think I understand now. If a trigger creates two outcomes that clash, this means that the trigger will not occur.

[ohthatpatrick]

That is definitely a true, useful takeaway!

Another way to put that is, "Sometimes I think I have either/or flexibility, until I realize that something else makes one of those two options impossible, thereby FORCING the other option to be the case."

When it comes to the trigger of a conditional statement, it's either true or not true.

If we find out that it being true leads to impossibility, then we are thereby forced to think that the trigger is NOT happening.