In need of help with this example

TheDeterminedC

I would say I am at the point where indicators and making diagrams has become second nature for me. But, this particular problem has my mind going in a loop. Logic makes more sense to me when I understand why certain negations are valid--i.e. DeMorgan’s Law and proofs. So any explanation for this example would be helpful.

"G cannot be cleaned until F is cleaned, unless F is cleaned second."

I will explain my reasoning so that one is able to point to my error.
To me, I view this problem in two parts, before the comma and after. Before the comma, using until as a group three indicator would cancel out the cannot, thus making the conditional G --- F. As for after the comma, I choose to use the unless portion (group three) to negate the previously stated relationship (G --- F). The negation of the sufficient condition of G before F would make it F before G -----> F2

My diagram would look like this. (F ---- G) ----> F2

Somehow this is wrong and I think it has to do with using three indicators instead of two, specifically hinging on the "until" term.

So my question is 1) is it wrong to use until as an indicator here and 2) when and how can I know to use an indicator or not.
Thank you so much!

10000019

This is how I see it:
If (F != 2)
F < G; // F is before G

If !(F < G)
F = 2; // (G < F) or (G and F concurrently)

I won't attempt to answer your question regarding indicators because I don't remember what the CC says. I'll tell you my thought process when I looked at it:
"G cannot be cleaned until F is cleaned, unless F is cleaned second."

1. My first thought is to record what happens when F is not second. We're just left with the "G cannot be cleaned until F is cleaned". That's straightforward.

2. Now I consider the situation where that is false (i.e. F is not before G). In that case, I know that F must be 2.

AudaciousRed

I think this is going to be a hard question to draw out. But this is how I understood it.

""G cannot be cleaned until F is cleaned, unless F is cleaned second.""
I saw this as two different problems in one. You have the first part "G cannot be cleaned until F is cleaned", which is then used in part two "unless F is cleaned second"

G cannot be cleaned until F is cleaned. Until is a negate sufficient term, so we take "F is cleaned", negate it and make sufficient.
F is not cleaned --> G cannot be cleaned. Contra positive of this, If G is cleaned ---> F has been cleaned. So, I think our thinking aligns up to this point.

Now... I see this problem as thus: "(F is not cleaned --> G cannot be cleaned) unless F is cleaned second." So, let's put that unless to work again. Negate and make sufficient, we get:
If F is NOT cleaned second --> (F is not cleaned --> G cannot be cleaned).
Or.. if we contra positive the whole thing... If G is cleaned --> F is cleaned --> F is second.
So.. basically, if G is cleaned first, then F is cleaned, then F must be in 2. If F is NOT in 2, F is not cleaned, so G cannot be cleaned. So anytime F is not in 2, F must be cleaned before G.
Writing it out, it seems... weird. But verbally, that last line makes sense to me.

Anybody else come to this conclusion? Are we both entirely lost here? LOL

keets993

"G cannot be cleaned until F is cleaned, unless F is cleaned second."

So let's break this down into two sentences. Let's read the first part:

"G cannot be cleaned until F is cleaned." I'll take 'unless' as my logical indicator and keep cannot as the negation. So the two ideas become:

"G is not cleaned" and "F is cleaned."

Apply 'unless' as group 3, negate sufficient.

G is cleaned -> F is cleaned.

So if I see that G is cleaned, F better be cleaned. If I see that F is not cleaned, then G is not cleaned.

This seems like a sequencing game so it would actually be F -- G. Because we're told that G cannot be cleaned until F is cleaned. So in terms of sequencing, F would go before G.

Now we have the second statement, "unless F is cleaned second"

[F - G] unless F is in 2.

So again, we apply the "unless" to [F--G] and negate it:

/F - G -> F2
/F2 -> F - G

Now...what's exactly does it mean to say that /F - G; or that F is not cleaned before G?

Well! G - F. You didn't say anything about double layer, so I'm going to assume it's single layer sequencing.

So we have two worlds:

G - F -> F2
/F2 -> F - G

There's a similar rule, I believe, in one of the games covered in the CC: PT 32, Section 3, Game 1. There's a couple others that employ similar mechanics if you want me to look and find them for you.

Lots of assumptions in my answer in terms of the set-up but I hope it helps (and is correct)

TheDeterminedC

@AudaciousRed @keets993 I agree with both of your interpretations of this problem and I appreciate y'alls help.

After viewing the steps in each of your analyses, I finally have found my mistake that will, without a doubt, help me next time I encounter a similar problem. Thank you for helping me get there.

When faced with G ----> F (after the "until" negation), I HAVE to remember that this diagram is referencing conditional logic and not spacial arrangements. It's used in this logic game specifically referencing spacial arrangements. In other words, the conditional diagram I originally wrote down G -----> F is not stating G is before F. Rather, the conditional merely represents the convoluted statement: "if there is a G then F has already been before it." I can understand in hindsight that this is not helpful at all and would most likely make me believe G is before F. Maybe a diagram of G ---> F ----- G is more visually representative. Even then, taking the "G ---->" off would make more sense.

Through all this really over the top analysis, I am now correctly left with F ---- G for the first negation. But more importantly, I understand why and will hopefully not make this mistake again.

What I have learned:

When in logic games, it makes more sense for the task to actually diagram the english explaining the rule in the form of what the end goal is: to make things simpler. For instance, if it's a grouping game, then blocks for the rule work well; if it's sequencing, then write down the relationship between the variables (i.e. G ----- F). In both of these instances one is better off tailoring one's diagraming to the situation then just always using conditional arrows.

Thanks again.