Rule Diagramming Question - December 1996 Game #4 Forum

[Paraflam]

Rule reads, "G is not advertised during a given week unless either J or else O is also advertised that week."

In the LGB analysis of this game, it says to diagram this rule as simply "GJ or GO" (with each being a vertical block).

However, in the section about conditional rules in the LGB, it says to use the "Unless Equation" whenever "unless" appears in a rule, which means:
1) Whatever term modified by "unless" (in this case "either J or else O is also advertised that week") becomes the necessary condition
2) The remaining term (in this case "G is not advertised during a given week") is negated and becomes the sufficient condition

So, after applying the Unless Equation wouldn't the diagram of this rule read "G ---> GJ or GO" (with GJ and GO in vertical blocks)?

Unless I'm interpreting this wrong (and I'm only beginning the LGB so that could be true), the difference between diagramming it the two different ways would be:
"GJ or GO" = Every time J or O is placed, G must be placed on the same week. Every time G is placed, J or O must be placed on the same week.

"G ---> GJ or GO" = Every time G is placed, then J or O must be placed the same week. However, the reverse is not necessarily true, meaning that if J or O are placed PRIOR to G being placed, it is not necessarily true that G MUST be placed on that same week, because J and O can occur with other variables on the same week, but G cannot.

In other words, why does the LGB not diagram this rule as a conditional rule? It appears that this difference would drastically affect the way the rules are applied in the game.

Any help is greatly appreciated!

[Jack Smirks]

"G ---> GJ or GO" (with GJ and GO in vertical blocks)?

I don't have that particular game in front of me but you should diagram it as above. If G has to be used or "in" you can skip the conditional statement and just use the blocks. Also, don't worry about the contrapositive because it's pretty self explanatory:

~ GJ block AND ~ GO block------> ~G

[Paraflam]

"G ---> GJ or GO" (with GJ and GO in vertical blocks)?

I don't have that particular game in front of me but you should diagram it as above. If G has to be used or "in" you can skip the conditional statement and just use the blocks.

Yes, I probably should've noted that this is an unbalanced underfunded linear game, where every variable must appear once and one of the variables appears twice. Why does this change the way you would diagram this rule?

EDIT: What does the ~ represent? Not familiar with that yet. Thank you for the help!

[Jack Smirks]

"G ---> GJ or GO" (with GJ and GO in vertical blocks)?

I don't have that particular game in front of me but you should diagram it as above. If G has to be used or "in" you can skip the conditional statement and just use the blocks.

Yes, I probably should've noted that this is an unbalanced underfunded linear game, where every variable must appear once and one of the variables appears twice. Why does this change the way you would diagram this rule?

Because then you know you must satisfy the sufficient condition- G must be used so you can just diagram the vertical blocks, no need to even confuse yourself with the conditional statement.

[Jack Smirks]

EDIT: What does the ~ represent? Not familiar with that yet. Thank you for the help!

~ = NOT

[Paraflam]

Ok I understand it now. Just so I know for the future, if a variable must be used in a game, and as a rule it must occur with another variable, you don't need to bother messing with the "unless", negating the sufficient condition, etc. and you can simply draw the two variables in a block?

[Jack Smirks]

Let me dust off the old LGB and walk you through it so it's clear. Okay, the prompt tells us that each of the seven products will be used at least once and that exactly one of the products will be used twice. So when I approach rule 3 I would look at it as a conditional statement and apply the "unless" equation:

G-------> GJ (vertical block) OR GO (vertical block)

the contrapositive would be ~GJ block AND ~GO block -------> ~G


But since we know that G must be advertised we know that we will have a GJ vertical block or a GO vertical block. So I would go ahead and diagram that:

GJ vertical block OR GO vertical block

At first it might be helpful to go through the two step process of diagramming the conditional statement and then figuring out that you must use one of the two blocks and diagramming accordingly. As you get better at games this sort of inference will be apparent and you will just skip straight to the second step and only diagram the blocks.

In this particular game though you have to remember that you can only use one of the two blocks so if you place J or O it doesn't automatically mean G accompanies them so you have to keep that in mind.

Does that clear things up?

[Paraflam]

Alright I've got it now. This was the first time I've run into a situation like that so I got a little mixed up, thank you very much for the explanation!