Grouping Setup Practice Drill #2

[leslie7]

Hi med2law,

You're dead on with this one! Really nice work.

Here's how you could represent your chain to avoid the trap you're talking about:

Screen Shot 2020-08-28 at 4.45.58 PM.png

The problem you're trying to avoid is the primary reason we recommend diagramming two (or more) necessary (or sufficient) conditions vertically rather than horizontally.

I hope this helps!

Hello - I've been looking through all the threads to avoid trying to start a new chat and I think this answer does well for my line of questioning (even though the answers might have been implied or hinted at in other responses, I couldn't find answers to them directly).

1. For context and as an example - I initially drew the diagrams as A->F->/E (realized that might not work) so then I did an arrow with two spears pointing to two necessary conditions (which I cant properly diagram here)
A --> F
-->/E (connect both arrows together from their starting points) .

It wasn't until I got to the answer key that I saw the relationship represented as "and". I didn't see this covered in the book so when do we use "and" in diagramming? Does the word "but" always mean "and" in diagraming?

The second and third question are related but I will separate them, hopefully for clarity.

2. I really like the picture shown here but let's say that we wanted to chain as many as possible variables, which was my impulse

The contrapositive of the first diagram is

/F or E /A /O &/S

If I wanted to link it with L E and /M

How do I represent all of the variables at their fullest capacity?

L E or /F /A /O&/S
E & /M

and on that note, why in the picture is "e or /f" not included to show the full chain? as in why is it omitted? (I'm wondering in the case that this question had a bunch of other questions that might make that piece of the chain relevant)

3. I noticed that med2law stated "I know the E + M portion above seems to imply that if E + M then A, but I didn't worry about that because E alone is sufficient for A" (so basically drop the & M )

but according to what I have read in the text book I am understanding that E AND M both have to occur together in order for the /A to be triggered. I'm not understanding how an "and" can be dropped from and how the E has now on its own, or in isolation has become sufficient for /A .

I like the picture because it does a nice job of showing how E alone triggers /A etc but I'm not understanding how or why the M does not have to happen together with E to trigger /A

[Robert Carroll]

leslie,

1. "and" and "but" have the same function in a purely logical context. In this situation, the necessary condition of the first rule is compound, which is why the two constituents are connected by "and". You can break this into two conditionals - A is sufficient for F and A is sufficient for not E.

2. I don't think showing everything in the chain together is very useful. You can represent it in an accurate way, but reading any inferences off such a complicated diagram is pretty difficult. So, to answer your question, I don't think I WOULD put it all together to represent all the variables. If I have to branch a conditional chain more than once or twice, it's probably getting out of hand, and I should represent some parts of it separately.

I'm not sure about the picture to which you're referring that lacks "E or not F". can you clarify?

3. This part of your diagram confirms that E alone is sufficient for A to be false:

E or /F /A

Note that the sufficient condition says that E or not F would be sufficient to make A false. So either one is sufficient for the result - that means that E alone is sufficient for A to be false. The reason for that inference is not related to M. That's why med2law noted that the M was superfluous in the representation. It was not an attempt to parse "E + M then A", but instead an attempt to show that the relations among E, F, and A already made E sufficient for not A.

Robert Carroll

[leslie7]

Hi Robert, Thanks for your reply.

I think I found out where my mistake was.

Here is what I have come up with..


O or S -> A -> F & /E (contrapositive) E or /F - > /A -> / O & /S

L-> E&/M - > /A -> /O & /S

(What I was trying to do was link what is in pink together... L E M and E or F) but I realize after that you can "drop" the /M and the /F because since we *know* we have E that's enough information to also know that we have not A and not O and not S

But even in this case I'm wondering with the L E & /M (for the purpose of the question E is sufficient but just for "extra knowledge") is it true that we also know that /M? as in E and /M occur together with the trigger of L? ( I know this is probably a yes just want confirmation)

additionally I am curious to know is it possible in an "or" statement for "both" to occur together? or does it only have to be one or the other to trigger a necessary condition e.g.

E or /F -? /A

We know if E -> / A (fair, that's enough)

We know if /F - >/A (fair)

but is it possible for "or" to also include E and /F as an option to have them both trigger /A ? (just curious on the possibilities)

Lastly based on the conditional chain I laid out the O or S in the sufficient condition turns into a /O and /S so I am wondering why it is that the inference is O or S <--/--> L as opposed to O and S <--/-->L

(I'm only saying this based off the rules we learned previously in the book, that any or becomes an and and vice-versa when writing out its contrapositive) In this case the O-S has been left as "or" in its contrapositive. Not sure here what I'm doing wrong can someone explain?

[Adam Tyson]

"Or" means "at least one," leslie7, so if we have "E or not F" in some chain, it would be possible for us to have E and also not have F. Both conditions could occur together, but only one or the other is required to occur.

The reason we treat the relationship between (O and S) and L as an "or" rather than an "and" is that if either O or S occurs, L cannot occur. To diagram it this way:

(O & S) L

Would mean you can never have L together with both O and S, but it would not preclude having L with just O or with just S. Since either O or S is, by itself, sufficient to get us all the way to proving that L is out, we use the "or" on one side of that double-not arrow. Another perfectly good way to diagram it is to break it into two such diagrams:

O L

S L

We know this is true, because if you have O, you must have A, and cannot have E, and thus cannot have L. Whether S is in or not is irrelevant. Same if S is in - O becomes random at that point.

[Mastering_LSAT]

Hi there,

I went through this drill, and realized that it touches upon an important linkage concept of conditional statements (or their contrapositives) by means of a common variable. After much reflection, I am still struggling to understand when we can/cannot link such conditional statements. I would greatly appreciate it if you could clarify the following:

1. Is there an easy-to-use rule which tells us when we CAN/SHOULD connect conditional statements (contrapositives of such statements) that have multiple sufficient and necessary conditions by means of a common variable?

2. Is there an easy-to-use rule which tells us when we CANNOT/SHOULD NOT connect conditional statements (contrapositives of such statements) that have multiple sufficient and necessary conditions by means of a common variable?

3. Do all of the following examples can be linked in a A --> B --> E chain?

[Dave Killoran]

Hi Mastering,

When it comes down to it, this is really a game of matching. You are looking to match like terms in the conditions. So, that is the controlling "rule" seek in both 1 and 2. It's one of those things that's easy to complicate, so I hesitate to make it more complex than that.

Looking at #3, consider how that matching works:

• 3.1. No Link. The terms are B+C and B+D, which don't match (you're missing a D for the second relationship).
  
  3.2. They Could Link through B. The terms are B or C (so either appearing anywhere will link) and B or D. If B appears from A, then the link would occur.
  
  3.3. They Will Link through B. The terms are B and C and B or D. So, even though the output of the A is BC, that triggers the B in the second statement.
  
  3.4. No Link. The sufficient in the second is B+D, and you don't have that output from the first relationship (you need D still).

Thanks!

[Mastering_LSAT]

Many thanks, Dave. Greatly appreciate your help. I need some time to digest your explanation.

A quick follow up. If, in the example 3.4, we changed C to D in the first conditional statement (meaning: A --> B or D), and leave the second conditional statement as it is now (B + D --> E), then we could connect the statements and have the A --> B --> E chain. Right? Why would this work?

I would greatly appreciate it if you could link/suggest some materials that could help with improving the understanding of conditional statements linkage. I feel it is too important of a concept not to have a strong grasp of.

Thanks again. Have a great day!

[Dave Killoran]

Well, it would work if A produced both of B and D (this is typically possible under or scenarios unless explicitly prohibited). But, if you only have one of the two, then it wouldn't link. The sufficient in the second term is "B+D," so to activate it you need both, not just one.

To help, I've altered my response above to try to make that "possible" connection a bit more clear.

Thanks!

[Mastering_LSAT]

Terrific. Thanks!

[waterisblue777]

I totally agree. I also feel this is too important of a topic to have superficial understanding. I am still going through the bibles and have not seen this topic in detail yet and skimming ahead I don't think there is much info on it. I know on page 297 (2022 edition), it mentions to look at book site for more information on conditional reasoning with multiple terms (didn't say anything about multiple terms conditional linkages tho) but I can't seem to find it.

I had some hiccups going through the bibles at few places but I was mostly able to figure it out myself but I spent a lot of time on this one problem and just couldn't understand the reasoning. The picture you posted of various combination of and/or conditional linkages was spot on root of this problem. I think a genuine detailed discourse on it would be very beneficial. If anybody is reading this in 2023, I would still like some pointers to resources if possible. Thank you in advance!

Many thanks, Dave. Greatly appreciate your help. I need some time to digest your explanation.

A quick follow up. If, in the example 3.4, we changed C to D in the first conditional statement (meaning: A --> B or D), and leave the second conditional statement as it is now (B + D --> E), then we could connect the statements and have the A --> B --> E chain. Right? Why would this work?

I would greatly appreciate it if you could link/suggest some materials that could help with improving the understanding of conditional statements linkage. I feel it is too important of a concept not to have a strong grasp of.

Thanks again. Have a great day!