Setup and Rule Diagrams

[colguin27]

Hello,

I was successful with my diagramming, and was able to find brilliant explanations of the game both on this forum as well as other websites. However, I feel that I am missing how to arrive at the key inference that W MUST be an area of expenditure that is reduced. I made a couple of hypotheticals showing that W could not be out.

1. NLMGP (IN) WSR (OUT) - This does not work because L and P cannot be selected together.

2. SPLMR (IN) NWG (OUT) - This is wrong because again, L and P would be selected together, AND LMR cannot all be selected at the same time.

Either W and S or W and G have to be out, because if G and S were both selected, then it would follow that W would have to be selected as well.

While my hypotheticals show WHY W cannot be selected, I feel as though it should not have required me to go to that length to prove why. I am not sure what I missed in my initial setup that would have allowed me to see this inference much quicker. If someone could point me in the right direction, it would be greatly appreciated.

[Adam Tyson]

menkenj - I think a template approach is the best way to approach this game, and yours are great! I did mine a little differently, based entirely on the LMR rule: one template with L and M in, one with L and R in, and one with M and R in. You'll end up with basically the same results, and a very efficient way to attach every question. Nice job!

And colguin27, I think that's the answer to your query, too. If we do templates for this game, we will see that in every case W has to be in. That's all we need to do - there is no need to test W in the Out group, because the templates have already laid out all possible solutions, and W is never out!

Without doing templates I think it's a lot harder to get to that inference (which is tested in the last question of the game), but at that point you could simply go over any local diagrams you did and eliminate wrong answers and perhaps only have to test one of two contenders. It's sometimes okay to not get every inference, because you may not need them all or, if you do, you will discover them when you need them.

[AspenHerman]

Hi again.

I'm very confused by the explanations for the set up of Grouping Game 1, number 4 and 5.

4. N (not)R and (not)S.
(not)R L and M
L and M (not)P
thus.... N (not)R (not)S (not)P
thus... N G, L, M, W

5. (not)L M and R
R (not)N
Thus: (not)L (not)N
(not)M (not)N

Can I please get a little more of an explanation as to how these inferences are obtained? In particular, number 5 is particularly confusing, especially with the last statement.

Sorry this is a little open ended. I don't know where my question begins.

Thank you!

[Dave Killoran]

Hey Aspen,

Thanks for the question! Just fyi, we'll likely move our posts over the actual game forum for these games, which is at viewforum.php?f=356 (and specifically, we'll move this one into viewtopic.php?f=356&t=8627). you didn't post in the wrong place, we just keep all questions for specific games compiled together since the same questions tend to come up

That said, let's look at what you've asked about here. The inferences in each case are caused by a chain reaction that connects the rules. So, when you looked at these, did you follow the rule connections? Or did it break down along way? If it broke (and I assume it did), where did that happen for you? I ask because I need to understand what didn't make sense to you here in order to identify the problem. For example, in #4, when N was reduced, did it make sense that R and S could not be reduced? Or was that issue? When R was then not reduced, did it make sense that L and M had to be reduced, or no? And so on. In other words, where in each chain did the inferences break down? Once I have a better sense of that, I can isolate what caused you trouble and help eliminate that as an issue going forward

Thanks!

[AspenHerman]

Hey Aspen,

Thanks for the question! Just fyi, we'll likely move our posts over the actual game forum for these games, which is at viewforum.php?f=356 (and specifically, we'll move this one into viewtopic.php?f=356&t=8627). you didn't post in the wrong place, we just keep all questions for specific games compiled together since the same questions tend to come up

That said, let's look at what you've asked about here. The inferences in each case are caused by a chain reaction that connects the rules. So, when you looked at these, did you follow the rule connections? Or did it break down along way? If it broke (and I assume it did), where did that happen for you? I ask because I need to understand what didn't make sense to you here in order to identify the problem. For example, in #4, when N was reduced, did it make sense that R and S could not be reduced? Or was that issue? When R was then not reduced, did it make sense that L and M had to be reduced, or no? And so on. In other words, where in each chain did the inferences break down? Once I have a better sense of that, I can isolate what caused you trouble and help eliminate that as an issue going forward

Thanks!

Hi! With more knowledge/practice on how on these games work, I reworked this problem and got to the inferences stated. Thank you for the leading questions, they were helpful.

[concrottrox11@gmail.com]

"The second rule bears further analysis. When N is reduced, neither R nor S is reduced, and it can be inferred from the contrapositive that when R or S is reduced, N cannot be reduced. Thus, N and R cannot be reduced together, and N and S cannot be reduced together. Consequently, we have written the rule in two separate parts to fully capture this powerful information."

Did we need to convert to the contrapositive in order to get the "double not arrow" between N and R and N and S?

[Dave Killoran]

Did we need to convert to the contrapositive in order to get the "double not arrow" between N and R and N and S?

Yes, every double-not arrow relies on knowing how the contrapositive works. If I say N S, then the contrapositive is S N , and it's easy to see that when one is present the other is not, which creates the double-not arrow.

You should learn to simply see this inherently though, and not rely on writing it out every time! It's kind of how you wouldn't do a long-hand calculation to added 8 and 5, if that makes sense.

Thanks!