Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Unbalanced: Overloaded game.

J92_Game_#3_setup_diagram 1.png

L is the only random fish in the game, and Z is the only random plant in the game.

Exactly three of the five fish must be selected. This means that only two of the five fish will not be selected. And, because exactly two plant species will be selected, exactly two will not.

Because X is a necessary condition for two other variables, you should examine the effects of the contrapositive. If X is not selected, neither H nor K can be selected. Therefore, if X is not selected, G, J, and L must be the three fish selected. When J is selected, then W is selected, and when G is selected Y cannot be selected, leaving Z to be selected. Hence, when X is not selected, only one solution to the game exists:

J92_Game_#3_setup_diagram 2.png

A very tricky inference involves Y and X. When Y is selected, G cannot be selected. This leaves only four fish in the selection pool (no pun intended). Because there must be exactly three fish selected, we cannot eliminate X from the selection list because removing X would remove H and K as well, which would leave an insufficient number of fish. Thus, if Y is selected, the other plant that must be selected is X. Consequently, if Y is selected, J cannot be selected, since J requires W, and from the first rule G cannot be selected, meaning that when Y is selected there is only one possible solution to the game.

J92_Game_#3_setup_diagram 3.png

This inference is tested on questions #16 and #17.

[srcline@noctrl.edu]

Hello,

I was going through this game and had a question on the linkage of a rule specifically between rules 2 & 4.

Rule 2 She cannot selected the H unless she selects the K
Rule 4 states IF she selects K she must select an X.

I diagrammed these rules as (2): H K, (4): K X
SO then I linked these rules as H K X which leads to H X

The book's diagram just linked the three variables H,K,X

Why isn't the H X correct.

Thankyou
Sarah

[David Boyle]

Hello,

I was going through this game and had a question on the linkage of a rule specifically between rules 2 & 4.

Rule 2 She cannot selected the H unless she selects the K
Rule 4 states IF she selects K she must select an X.

I diagrammed these rules as (2): H K, (4): K X
SO then I linked these rules as H K X which leads to H X

The book's diagram just linked the three variables H,K,X

Why isn't the H X correct.

Thankyou
Sarah

Hello Sarah,

I'm not sure what your'e asking here. H K X is correct. H X is also correct, though it omits the K in between. So when you ask, "Why isn't the H X correct", I am not sure what you are saying. If you could clarify, that would be helpful. Thanks!

Hope this helps,
David

[srcline@noctrl.edu]

Hello David,

I was wondering why the book did not show the inference of H X? Maybe I am missing something?
Thankyou for your time
Sarah

[Dave Killoran]

Hi Sarah,

I don't have this in front of me, but I suspect that the reason is that it's so straightforward that we expect you to know it inherently. A similar situation would be us not showing a contrapositive for a really basic rule, like A B. We'd simply expect you to know it in the basic cases.

If you have A B C, in most cases I'd say that writing A C out would be something I'd suggest students do at the start of their studies (to make sure they have it), but that as time goes on they could drop writing that out (since they'd have that recognition locked down, and they could save a few seconds by not writing it).

Please let me know if that helps. Thanks!

[srcline@noctrl.edu]

Hello Dave,

I thought that might be it because I had gotten the question right, but I wanted to double check.

Thank for your help.
Sarah

[lsatjourneygirl]

Hello,

I have a question about the first rule "If she selects the G, she can select neither the H nor a Y"

I understand that this rule means that G cannot be selected with H or Y. I also realize the rule implies that at least H or G must be out and at least G or Y must be out. This is more of a fundamental logic question, but H Y and G could all be out, correct?

Also for clarity during a game, would it be best to automatically write H/G and G/Y in the out group right away?

[Nikki Siclunov]

lsatjourneygirl,

You're right. The rule you're asking about can be summarized as follows:

• G H, Y

It also breaks down into the following two rules:

• G H
  G Y

The rule does not mandate that any of these variables be selected. All we know is that G cannot be selected with either of the other two variables. The following selection combinations are therefore possible:

• Nothing selected
  G alone
  H alone
  Y alone
  H Y

If I were you, I probably wouldn't do the split dual-options in the "out" group. While technically correct, they can mislead you into thinking that at least two variables must be out: H/G and G/Y. However, it is possible that G alone is out, with both H and Y in.

Hope this helps!

Thanks,

[Xantippe]

Overthinking the diagram messed me up. I stacked the fish and plants group horizontally and separately with their respective in and out groups but, because the variables overlapped (fish subscript plants/plants subscript fish), I probably confused myself and spent more time on the game than necessary.

Was their something I should have seen to indicate that this game did not require a stacked set up?

Thank you!

[Jeremy Press]

Hi Xantippe,

As far as I can tell from your description (and let me know if I'm reading you wrong), the only difference between the setup you describe and ours is that you depicted the "out" slots for both the fish and the plants (whereas our diagram in the setup you see above does not). I'm a little confused by your statement that the variables "overlap" and that "fish subscript plants" and vice-versa. It's true the game identifies two separate categories of variables to track in the group (so you have to keep the fish and plants separate in the group diagram), but both your described setup and our setup account for those categories.

Here's something you may want to change in a future game like this: we do not ordinarily depict "out" groups in our grouping-game diagrams, because it streamlines the setup and gets you focused on the thing you're most concerned to identify in a grouping game: the variables that actually are part of the group. That streamlining may help to avoid confusion. Let me know if I haven't covered everything you were asking about, as I was a little uncertain!

Jeremy