Linear Games Rule Diagramming Drill #8

[RJF]

In the LG Bible, Chapter 3, Question #8 on page 73: "If A sits next to B, then B does not sit next to C"

I understood this to mean: A and B are a rotating block (i.e., either can be first as long as their next to each other). Same as for B and C. But the response to the question indicates that they are regular blocks, not rotating blocks.

How am I to know that "next to" indicates fixed position? It didn’t say A was immediately before B, just that A was "next to" B. The wording of "next to" leads me to understand this as a rotating block (as in: AB or BA). I need to understand why this question indicates fixed position, rather than rotation. Is "consecutive" the only indicator for rotation?

Thank you

[Jonathan Evans]

Hi, RJF,

Great question. What happens here is that you can take the symbolization one step further than the initial conditional representation to create a powerful "Not Block." To wit, as the book suggests, many students may start with a conditional representation of this clue. Such a conditional could be correctly represented thus:

• [AB] OR [BA] [CB] & [BC]

Consider these two scenarios. Suppose for example:

A B _
1 2 3

What does this scenario imply about C?

Likewise, suppose:

_ B A
1 2 3

What does this scenario imply about C?

In the former situation, C cannot be in the third space. In the latter example C cannot be first.

Thus, you could go one step further than the initial conditional to represent this clue as two not laws:

[ABC] & [CBA]

If you do the conditional and don't take it this extra step, it's not really a big deal. However, not only does the not block give a direct visual representation of what cannot be true, but it also helps obviate potential errors in conditional reasoning to which we are all susceptible from time to time.

Please follow up with further questions!

[Adam Tyson]

I'll add to Jonathan's explanation that the explanation in the book is suggesting that if a student were to diagram AB BC, they would be doing it incorrectly. The two suggested not-blocks of ABC and CBA capture exactly what you believed to be true, that the potential AB block and the potential BC block are indeed "rotating". If you have AB, then you cannot have C immediately after B; if you have BA, you cannot have C immediately before B. In addition, if you have BC, then you cannot have A immediately before B, and if you have CB, then you cannot have A immediately after B.

Your understanding was correct about the rotating nature of those potential blocks, RJF! The explanation was in agreement with that interpretation and was warning against treating them as fixed blocks.

Good work!

[RJF]

Hello Jonathan and Adam,

Thank you both for taking the time to respond - your explanations have been helpful.