Setup and Rule Diagrams

[eober]

Hi,

I just want to make sure if my inferences are correct in this game.


I made the inferences:
U W (from W S and S U)

R T (from T W and R W)

W Y (from R W and R not Y) because if W is there, R is not, if R is not then Y is.

Y R (from Y not R)

Does the inferences I made make sense? I get confused when combining a rule with a double arrow. Could you explain as a general rule how we make different inferences from double arrows and double not arrows?

Thank you!

[David Boyle]

Hi,

I just want to make sure if my inferences are correct in this game.


I made the inferences:
U W (from W S and S U)

R T (from T W and R W)

W Y (from R W and R not Y) because if W is there, R is not, if R is not then Y is.

Y R (from Y not R)

Does the inferences I made make sense? I get confused when combining a rule with a double arrow. Could you explain as a general rule how we make different inferences from double arrows and double not arrows?

Thank you!

Hello,

One might do them differently, something like u s w slash t, slash r, with the slash r y. (Because we know that slash y r)

As for "different inferences from double arrows and double not arrows", the first is about "love", the second is about "hate". Make sure you correctly track any arrows coming in or out of double arrows, e.g., if A B, and C A, then you can assume that C B. But if there were A C, you can't automatically assume that C B.

David

[Zierra28]

I just wanted to clear up a few uncertainties please:

~In order for W and S to have a double arrow relationship, the rule would instead state 'W and S always appear togther?'
~Is there another way to drill into my head that rule 1 means S----->W and not the other way around?? I SEE it, and I read the explanation, but I'm not confident, given a similar example, I wouldn't make the same mistake of diagramming the opposite.
(I'm having the same issue with the other rules in this game as well). I'm referring to the list of words for 'sufficient' and 'necessary' variables, but even then, it's still a BIT blurry.

Thanks!

[BethRibet]

Hi Zierra,

Thanks for the question.

Confusing a classic conditional relationship (i.e. one condition is sufficient, the other necessary), with the two being mutually required (a double arrow) is a common mistake on the games.

Yes, to be a double arrow, it would need to say "Wendy and Selma always appear together" or something equivalent. It could for instance say, "Wendy appears in every photograph Selma appears in, and Selma appears in every photograph Wendy appears in." The first part is already present in the rule, but note that the second part is not. The first part means: If S --> W, and the second part meas if W ---> S. So try to remember that to get a double arrow, you need both to be stated.

Mostly, to get more clear on this, I would just try to make it a habit to ask, when you see two variables grouped together, to ask yourself -- is this a single sufficient and necessary relationship, or a double arrow. If you can just remember to routinely check, it should get easier to avoid making the mistake!

Hope this helps!
Beth

[Echx73]

Hello Team PowerScore,

I have some questions on Game #3 December 2004 found in the LGB on Page 309. My question is regarding the rules.

Rule #1 is S --> W

Rule #2 is U ---> S

Rule #3 Is where I am having a problem. This rule is presented exactly like rules 1 and 2 but it has a negative condition. I am told by the LGB on Page 244 you are able to write the contrapositive when one of the conditions is negative. Does that in turn mean you cannot write a contrapositive statement when you have two positive conditions ( I have been writing contrapositives for two positive condition statements)?

Your team has been such a help!

Respectfully - Eric

[Ricky_Hutchens]

Hi Eric,

Let me start off by saying that you have been doing it right, you can absolutely write the contrapositive when you have two positive conditions. If you have a rule that says "If A then B," you should write:

A ---> B and /B---->/A (with a pencil you can actually strike through the letters).

In this particular problem, we know that R appears in every photograph that Y does not appear in. So if Y is missing then R is present. Thus

/Y ---> R.

But the contrapositive is also true:

/R ----> Y.

This rule is telling us that we must one or both of R and Y.

Hope that helps.

Ricky Hutchens

[Echx73]

Thank you, Ricky. I do have one more question on this same question.

"Wendy appears in every photograph that Selma appears in"

S ----> W

Is there a contrpositive?


Selma appears in every photograph that Umiko appears in"

U------>S

Is there a contrapostive?


Thank you!

[Dave Killoran]

Hi Eric,

Any basic conditional statement in the A B form has a contrapositive: simply reverse and negate the terms. Thus, in your two examples, it becomes:

• W S
  
  and
  
  S U

The contrapositive is always present when there is a conditional statement, and it should be something you recognize as inherently present at all times (really, to the point of not thinking about it much; you should just know it's there all the time). The example I use is that's like looking at two sides of the same coin: they appear different, but intrinsically they have the same value.

Please let me know if this helps. Thanks!

[DlarehAtsok]

In games such as the third one of December 2004 (single selection undefined group, can be found on page 309 of the 2015 Bible), I find it easier to organize the information through conditional chains (e.g. U --> S --> W --> not R (and independent branch which gives not T) --> Y, while Z is a floater (somehow I write the rules and the inferences together). Are there any objective cons to this way of setup setting?

[Robert Carroll]

Dlareh,

The conditional diagram is perfectly fine. In addition to it, it helps to represent the pairs that can't be in a photograph together with double-not arrows. This allows you easily to see that these pairs don't work together. Also, the rule about R and Y is useful to represent separately so you know each photograph must contain at least one of them.

Robert Carroll