Setup and Rule Diagrams

[Xantippe]

Yes, you are correct about what I meant by 'overlap'. There are two different categories Fish and Plants (I was thinking Algebra, one cannot combine apples and oranges) but, one can combine fish and plants, indeed that is what the game asked us to do.

I don't know why I thought subscripts and stacking would make a good diagram. In the end I answered most of the questions linking the conditions, making inferences and testing them within their respective scenarios. My original 'stacked' diagram was only useful for maybe two questions, I am sure I did not capture all the main features of the game.

To fully understand your response; I re-did the Aquarium game with no subscripts and (my so called) stacking, wow how nicely it flowed. I also re-did a proper linear stacked game from Lesson 4. Both games are so different, is it safe to say that stacking is for linear games only?

Thanks so much for your time and insights!

Edit to add: I just now worked L7 (7-32). Game 1, June 2003 where stacking, grouping and linear techniques are used. So, for combination games we use more than one technique but, for a strictly linear game, stacking is not generally used?

[Claire Horan]

Hi Xantippe,

Variable sets are stacked in advanced linear games and in combination games with more than two variable sets. Reviewing Lesson 4 and thinking about why advanced linear games are set up this way will help you understand how to diagram. In an advanced linear game, you may have three variable sets, such as specific contestants, their ranks, and whether they are male or female. You are given rules that relate contestants to their gender, contestants to their rank, and ranks to gender, but you would not be able to visualize all of these rules if you used only a basic linear diagram. If you knew that Contestant A was 5th place and that the fourth place contestant was male, how could you put both of these in a basic linear diagram? Advanced linear diagrams help us visualize this information by having one row be the contestants themselves, and the row above that be their genders, with the ranks running across the bottom.

Now contrast this with the fish and plants grouping game. They are being put together in one group. Although you happened to diagram this in a way that looked similar to the stacking you've done in advanced linear games, there was actually no way to use an advanced linear setup for this game because it lacks linearity--that is, there is no order. The plants and fish are in the group or they are not.

The takeaway from this whole discussion: When you are puzzling through how to make a particular diagram, first identify what type of game you have and use Powerscore's diagram for that type of game. But if the game is of an uncommon type, focus on drawing a diagram that helps you visualize the relationships between the variable sets.

Good luck!

[Kelly R]

Hi PS,

I've done this game multiple times and struggle to see the J--> XHKL inference each time. What should tip me off to the fact that this inference involving J and X is present? If I play around with the variables for long enough, this inference reveals itself, but this clearly isn't feasible under timed conditions. Is this an integral inference to make in the set-up phase, or is this an inference that we might be better served discovering once we're in the questions (for the sake of time)? Thanks so much.

[Adam Tyson]

Where are you seeing that inference, Kelly? J requires W, but it does not require X or H. A perfectly acceptable solution to this game would be JGL WZ, for example. Was this in relation to a specific question?

[nosracgus]

Hi PS,

I think I'm confusing myself when diagramming this game. The "unless" portions are really tripping me up. I thought I should do the Unless Equation here by making the W the sufficient condition and J the necessary (and same for H/K relationship). As I worked through the problem I realized that was obviously wrong so I just ignored my diagram and luckily got most of the questions right, but it took a long time (as expected!). I've looked through the explanations but I'm still confused on this specific point. Please let me know what I am missing here/why the Unless Equation doesn't apply?

not W J
not J W

Thanks!
C

[Adam Tyson]

The Unless Equation definitely does apply here, nosracgus, so the issue may be a misunderstanding of how that works. "Unless" will indicate the Necessary Condition - in the case of the third rule, that means that W is Necessary and goes to the right of the conditional arrow. The next step is to take the other part of the rule and negate it, and that negated element becomes the Sufficient Condition and goes to the left of the arrow. In that same rule, that means we take the statement "She cannot select the J" and negate it to turn it into "If she does select the J." Negating a negative means making it positive! That creates this representation for the third rule:

J W

It looks like you may have forgotten the step of negating the first part of the statement. I hope that clears up any confusion!

[nosracgus]

Ok this makes a lot of sense. I had everything backwards. Thank you!

[kenlars5]

Hi there,

Can you also make the inference that either K or G MUST always be in? If K is not in, G must be in and if G is not in K must be in? I made this inference but have yet to see the same one being made by anyone in these discussions posts. Just wanted to double check that I wasn't doing something wrong here.

Thanks!

[Paul Marsh]

Hey kenlars! That is true, one of K or G must always be in. In fact, we can make the stronger inference that either K is in, or else all of G, J, and L must be in.

This follows from our second rule in this game: H K. The contrapositive of that rule is: Not K Not H. In other words, if K is not in, both K and H must be out. But remember that our "Out" group for the fish only has room for two spots. So that means that if K is not in, our "Out" group is completely filled by K and H, and so our other 3 fish (G, J, and L) must all be in. To sum up: if K is out, our Fish In group is G, J, and L. And on the flip side - if any of G, J, and L are Out, that means K has to be in (because now there's no room in our Out group for both K and H). So again: either K is in, or else all of G, J, and L must be in.

Nice going on that inference!

[emilyjmyer]

Hi!

I am bit confused with first rule regarding G, H, and Y.

I am not sure if I diagrammed it right. I see on the explanation a double not law was used. Those honestly confuse me a bit and I tend not to use them.

I just was not sure if it should be diagrammed like
J--> not H and not Y
or
J--> not H or not Y

And then I know that this affects the contrapositive but did not know what to make the contrapositive without the actual diagram.

Thanks!