Conditional Reasoning Diagramming Drill #11

[Dave Killoran]

The sentence in this problem is as follows:, "G cannot be cleaned until F is cleaned, unless F is cleaned second."

This can be broken into two distinct parts (as separated by the comma in the middle):

• 1. "G cannot be cleaned until F is cleaned." As written this would be diagrammed as F G.
  
  2. "F2." This needs no further analysis.

In reading this problem, note that there is an "unless" in the middle of the problem, modifying F2. Thus, we can begin a diagram here with F2 as the necessary condition, since "unless" introduces a necessary condition:

• Sufficient Necessary
  
     F2

As per the Unless Equation, the remainder is negated and becomes the sufficient. Thus, we negate F G, which becomes G F. That then is the sufficient condition:

• Sufficient Necessary
  
  G F    F2

This is a tough one, so please let us know if you have any questions!

[macklo_]

For sample question 11, it states:
"G cannot be cleaned until F is cleaned, unless F is cleaned second."

The book says the original is: If G is cleaned before F, then F is cleaned second.
It says that the contrapositive is: If F is not cleaned second, then F is cleaned before G.

I am a little confused about how this assumption is made. I don't see this in the statement. To me, I see it as:
Original: If F is not cleaned second, then F is cleaned before G.
Contrapositive: If G is cleaned before F, then F is cleaned second.

This sentence says that if F is cleaned second, then G does not have to be cleaned after F, but it does not say that if F is cleaned second, G MUST be cleaned before F. I am seeing it as if F is cleaned second, G could be cleaned anytime.

Can someone explain to me why I am wrong?

[Adam Tyson]

I can't tell you why you're wrong, macklo_, because you're not wrong! Everything you're saying is correct, and it all matches perfectly with what the book is saying. There's no conflict, just using different words to say the same thing.

First, with any conditional relationship, the contrapositive and the original claim are logically equivalent statements. They mean the same thing, and you can diagram them either way. There's no need to concern yourself with which claim is the "original" and which is the contrapositive, because they are really just two ways of saying the same thing.

One good example of this is in the use of words like "unless." Our methodology is to teach that it indicates a necessary condition, and the negation of the other claim in the relationship is sufficient. If I see "I will attend the wedding reception unless I am needed at my office," using our methods I would diagram "at reception needed at office." But many other sources teach a different approach, the "if not" approach, whereby "unless" is interpreted as meaning the same as "if not," negating that condition and making it sufficient. That approach would cause you to diagram that same statement as "needed at office at reception." You can see that these two approaches lead to different "original" diagrams and thus different contrapositives, but neither is wrong. With either approach, you arrive at a statement that means exactly the same thing! The two results are the contrapositive of each other, and are logically equivalent statements.

Everything you said is accurate, and so is the book. You're just getting there a different, equally valid way. Good work!

[dsamad]

Hi Dave,

Thank you for your explanation. I have a question relating to the nested conditionals on LR v. LG. At first, when I encountered this drill, I treated it as a nested conditional and attempted to diagram it as:
Not(G->F) -> F2
Then after looking at the provided explanation, I realized that the first half of the sentence is treated as a sequencing rule. Should I understand that there are no nested conditionals on LG? Moreover, should I understand that sequencing rules could be presented in conditional language?
Further clarification on this matter would be much appreciated.

Regards,

[Paul Marsh]

Hi dsamad! Good question.

Knowing exactly how to negate a conditional is beyond the scope of formal logic required for the LSAT.

But just in case you have some formal logic background or you find the topic interesting (please ignore this short paragraph otherwise) - the negation of (A B) is actually (A + B). For example, let's say we have the following conditional : when the Cubs win, I have a beer. This would be expressed as: Cubs win beer. The negation (logical opposite) of that conditional would be: the Cubs won and I didn't have a beer. In logic terms: Cubs win + beer.

The only circumstance in which negating a conditional might come up on the LSAT is in the case of a nested conditional, like you mentioned. For example, NOT(A B) C. It's unlikely that you'll see an LSAT question where you need to parse out a nested conditional. If you do, here's a shortcut. That nested conditional I just mentioned? The one that goes NOT(A B) C? Let's just re-write that like so - A B or C. Boom, that's the shortcut! How did we get there? Don't worry about it! A bunch of behind the scenes formal logic mumbo jumbo. But I promise it works. So let's try it out with the nested conditional that you mentioned:

Not(G->F) -> F2

Just like we did above, we'd simplify it to:
G (F or F2)

And that's all there is to it! You asked if there are no nested conditionals on Logic Games. I don't know if I can say never, but I don't believe I've ever seen one. (It's more likely that there's an easier sequencing rule there, or you might be misreading something.) But again, if you ever find yourself wrestling with a nested conditional, the shortcut above is your best way out.

As to your final question: yes, sequencing rules can always be expressed as a conditional (if you want to make life challenging for yourself)! For example, "A finishes the race before B" is of course a sequencing rule and would be normally expressed as "A - B", but it can also be expressed in conditional format like the Bibles example: "B cannot finish the race until A finishes the race". Or it can be expressed in even clearer conditional language: "B finishes A finished".

Conditionals are nothing more than a tool (oftentimes a very helpful one!). Knowing how to use a tool is important, but equally important is knowing when to use the tool. Will expressing the sentence in a conditional help you attack the problem? There are many instances where a sentence could probably be shoehorned into conditional format, but doing so doesn't help you attack the problem at all. Always being on the lookout for conditionals is a good instinct to have, but don't force it!

https://blog.powerscore.com/lsat/bid-33 ... o-diagram/

Hope that helps.

[dsamad]

Thank you so much! This is of great help!

[leslie7]

I have a question on the process of this answer (I'm trying to understand what "negation" is meant in this response.

This can be broken into two distinct parts (as separated by the comma in the middle):

1. "G cannot be cleaned until F is cleaned." As written this would be diagrammed as F --- G.
when I read this though and if I apply the rules it would be G ---F because the negation of G cannot be clean is G Can be cleaned and after the word until we have the NECC condition - so I am not clear on this step and how it came about. It seems like I would come to F---G if I wasn't studying for the LSAT I would think yes, F has to be done before G is cleaned up but that doesnt apply the logical rules or am I missing something?

2. "F2." This needs no further analysis.

As per the Unless Equation, the remainder is negated and becomes the sufficient. Thus, we negate F --- G, which becomes
G ---F. That then is the sufficient condition:
Here i am not sure how flipping F---G to G--F is a negation? Even though we reached the same results I'm just concerned I'm mis understanding the process here and how negation is being used? I'm afraid i'm not understanding negation and I don't want to mis-apply the rules to similar questions in the future - sorry for the wordiness

[KelseyWoods]

Hi Leslie!

I think you're confusing sequencing rules with conditional rules. The first rule F G is a sequencing rule, not a conditional rule. Notice that it consists of a sequencing dash ( ), not a conditional arrow ( ). It just tells us that F must be cleaned before G.

You are correct that "until" is a necessary indicator. The conditional way of diagramming the statement: "G cannot be cleaned until F is cleaned." would be something like this: G is being cleaned F is already clean. But because this is a rule from a sequencing game in which we know both G and F are going to be cleaned and we just need to figure out the order, we can just diagram it as a sequencing rule. "G cannot be cleaned until F is cleaned" simply means that F must be cleaned before G.

To negate a sequencing rule in a game in which there can be no ties, you just flip it around. The negation of F before G would be that F is NOT before G. As long as there can be no ties in the game, that simply means that G would then be before F.

Thus, the negation of F G (F before G) is G F (G before F).

Hope this helps!

Best,
Kelsey

[leslie7]

Hi Kelsey,

This is a great explanation and it was very well written, I'm really glad you understood my question and you were able to clarify - I can see where I erred now pretty clearly.

As a follow up,

I may have gone through this in the book already and based off your answer I can gather that a sequencing game is (F--G) as opposed to a conditional (F-->G) but could you explain what the different rules are for both games (if any) apart from the differences in negation you just mentioned?

Also, I did see this on another thread but if you could explain "no ties" that would be great as well.

Thanks so Much!!

[Jeremy Press]

Hi leslie,

A sequencing rule is simply a rule that states that one variable must be somewhere before (or after) another variable within a given sequence. Thus, that kind of rule establishes a basic ordering relationship between those two variables. We use the dash diagram between the two variables to represent a couple basic facts: (1) the variable to the left of the dash has to appear in the sequence "before" the other variable, and (2) we don't know the precise distance between the variables (they might be very close, or they might be far apart). You'll find sequencing rules in Pure Sequencing, Basic Linear, Advanced Linear, and Grouping-Linear Combination games (basically, any game where you have to track the ordering relationship between variables).

In general, a conditional rule is a rule that creates a "conditional relationship" between two occurrences in the game. The sufficient condition (which we diagram on the left side of an arrow) is a condition whose occurrence indicates that a necessary has to occur. The sufficient condition's occurrence thus depends on the occurrence of the necessary. The necessary condition (which we diagram on the right side of the arrow) is a condition whose occurrence is required in order for the sufficient condition to occur. A conditional rule, always diagrammed with an arrow, can be used in any type of game, including any Linear game and any Grouping game. In a linear game (with sequencing rules), the conditional rule is basically a way of saying that, if one thing occurs, then you have to make sure another thing occurs as well. What those "things" are will vary from game to game. Sometimes, though, as with the rule Kelsey was discussing, the conditional rule will, in practical effect, affect the game by forcing one variable to go before or after another variable. If that's what the conditional rule does, then you can depict the rule using your simple sequencing diagram (discussed above).

"No ties" in a game simply means that 2 variables cannot occupy the same spot in the game: in other words, they cannot occur at the same time as each other. The majority of ordering games are set up this way, and this fact is often established using additional language in a scenario (something like "no two runners finish at the same time," or "no two trucks arrive at the same time," etc.). But you have to be careful because in some games, this specification isn't present, and then you have to allow for the possibility that two variables could happen "at the same time" (or occupy the same slot in the game).

I hope this helps!