Valid transitive conclusions questions Forum

[BrownieD]

Hey ya'll, I have a quick question to find out if the explanation I made for myself is correct.

Imagine these two arguments:

1. A-->B
2. AT LEAST 4 Bs are Ys
---
3. Answer: I can't make a valid conclusion.

BUT

1. A-->B
2. AT MOST 4 Bs are Ys
---
3. I can conclude that at most 4 As are Ys

Is the difference because "at least" is too vague to make a conclusion and "at most" is limiting enough?

Is there a better way to diagram "at most" and "at least" by the way????

And thanks in advance for any input!

[sashafierce]

I don't think that you can make a valid conclusion under both scenarios, we don't know enough about B to make any valid inferences. We need to know that All B's are Y in order to make any valid conclusions.

[BrownieD]

The thing is, this was the answer in an lsat book! I don't know if it has something to do with contrapositives or what.

[axel.foley]

You will really never come across something like this on the LSAT (coming from someone who has drilled every Cambridge LR packet & done PTs 40-72).

FWIW, like the above poster I'm also unsure whether #2 is a valid inference. The way to diagram this in the "LSAT sense," if there is one, would be A --> B <-Some-> Y. In this case no inferences can be made.

[sashafierce]

I'm not an LSAT book so Im not disputing what the books say per say but I learnt the hell out of those statements so I can tell you:

A some B
B----> C
Valid conclusion A some B

A most B
B------>C
Valid conclusion A most C

A----->B
B------>C
Valid conclusion A----->C

Main point, in all instance we know All Bs are Cs which allows us to make a valid inference. Also, if I'm wrong can someone correct me.

[axel.foley]

I'm not an LSAT book so Im not disputing what the books say per say but I learnt the hell out of those statements so I can tell you:

A some B
B----> C
Valid conclusion A some B

A most B
B------>C
Valid conclusion A most C

A----->B
B------>C
Valid conclusion A----->C

Main point, in all instance we know All Bs are Cs which allows us to make a valid inference. Also, if I'm wrong can someone correct me.

You are definitely correct -- this is what the LR Bible refers to as the "some/most train." The "all" arrow has to lead away from the "some/most" arrow to draw a valid inference. OP, if this isn't clear I would strongly recommend the LR Bible or, even better, the 7Sage full course (J.Y. has about 20 lessons in which he discusses valid & invalid inferences that come up on LR).

[sashafierce]

I recommend the 7sage course as well. That's where I learnt it, he has a lot of useful drills that help you fully understand the concept.

[anon sequitur]

Is the difference because "at least" is too vague to make a conclusion and "at most" is limiting enough?

Is there a better way to diagram "at most" and "at least" by the way????

You've got the right idea. The second pattern you gave yields a valid inference that at most four A's are Y's. Notice how vague and almost insubstantial a conclusion that is, it doesn't even imply that any A's are Y's. It just guarantees that it's less than 5 of an indeterminate number of A's can be Y's.

I imagine the point of the exercise in whatever book you're using is to show you exactly what commitments phrases like "at most" and "at least" create.

[BrownieD]

Okay, I see I made a mistake with the first one. It should matter whether it says "at least" or "some," right? Because I couldn't make a conclusion from that.

"At most" seems to be a different case because it limits, but if this isn't likely to show up on the test, I won't worry about it too much.

I'm actually taking the 7sage course as well! Just drawing from a lot of material, and this problem set confused me a bit.

[mornincounselor]

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