But not Both

[Heather]

Hello!
Can someone please explain how 'but not both' is diagrammed?
For instance, in Preptest 51, Question 6, the last rule reads:
F is more expensive than G, or else F is more expensive than H, but not both.

How would this be diagrammed and considering this is a sequencing game would we form a sequence out of this last rule as well?

Thanks!

[Dave Killoran]

Hi Heather,

"But not both" simply precludes both possibilities from occurring. So, whatever representation eliminates that outcome is fine.

With this specific type of LG rule—which is covered in the Conditional Sequencing section in the LGB—what the wording does is create two mutually exclusive possibilities. Let's look at it more closely by breaking the rule down:

• F is more expensive than G ( F > G)
  or else
  F is more expensive than H (F > H )
  but not both.

So, in the first case, F > G. When that occurs, you can't have F > H (due to the "but not both"), and since this game doesn't have a tie possibility, that means that H > F. So, when F > G, then it is also true that H > F, which ties together to create H > F > G.

When the second case occurs, then F > H. When that happens, you can't have F > G (due to the "but not both"), and since this game doesn't have a tie possibility, that means that G > F. So, when F > H, then it is also true that G > F, which ties together to create G > F > H.

Since one of the two must always occur (the rule states F > G or else F > H), that means that the game is effectively split into two entirely different directions. The diagram for that would be:

• H > F > G
  or
  G > F > H

However, given that this sends the game down two very different paths, you'd make diagrams for each option, and add the other rules onto each possibility, creating an Identify the Templates situation.

Please let me know if that helps. Thanks!

[Heather]

Thanks a bunch Dave!