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dalaal on February 22, 2020

Regarding argument completion drills

In Argument Completion Drills, I did not quite understand the following conclusion: P1: X -> not Y P2: X -> Y Con: X does not exist How did you reach this conclusion, what is the logic behind it? Another question is regarding the following drill: P1: A exists P2: Not B -> not C P3: A -> C Is the conclusion only the fact that B exists, or should we say both B & C exist? On the LSAT, are conclusions only the end result since perhaps the fact that C exists could be considered as a subsidiary conclusion?

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on February 23, 2020

Hello @Dalaal,

I think that the first one is kind of a trick question. X comes with two necessary conditions that are contradictory: Y and not Y. This means that X is impossible, it cannot exist. Let's try taking the contrapositive of the premises.

P1: Y - -> not X
P2: not Y - -> not X

If Y exists or Y doesn't exist, either way we have the same conclusion: X does not exist.


P1: A exists
P2: not B - -> not C
P3: A - -> C

Taking the contrapositive of P2, we have C - -> B.
A - -> C - -> B
A exists, therefore B exists.

For the purpose of these drills, we want to use all of the premises. Because of this, I can tell that [B exists] is the answer they are looking for. It is the main conclusion.

However, you are correct that [C exists] is another possible conclusion. I would call it a sub-conclusion! Good thinking. Sometimes a logical reasoning question will ask you to identify a subsidiary conclusion, so it is important to understand what this means.

on May 16, 2020

Thanks so much for the above explanation. Further to the above, could I clarify whether an invalid conclusion is the same as saying X does not exist?

To just check my understanding -
P1: A --> B
P2: B --> C
P3: A does not exist
C: B and C do not exist - is that the same conclusion as saying "no valid conclusion"?

In addition, I would be very grateful if you could please walk through the following:
P1: A --> not B
P2: C --> B
P3: not D --> A
C: ?

How do you connect the above using contrapositives - for the conclusion I got, not B --> not A --> D --> not C. Where did I go wrong here?

Many thanks again!

on May 29, 2020

Please can I follow up on this. Thank you.

on June 2, 2020

Please could I follow up on this. Thank you!

Brett on July 2, 2020

I'm trying to wrap my head around valid conclusions, too.

For the first argument, it almost seems impossible to conclude "B and C do not exist" because that would seem like we're using a necessary condition to calculate a sufficient condition.

I thought these S-->N conditions were a one-way street. Just because we don't have A doesn't mean that there isn't another sufficient condition to give us B. If there were, then we'd potentially have B and C.

It looks like an invalid argument.

Brett on July 2, 2020

@Anna2020 For the second one, I think it's possible to just write out the premises with their contrapositives and look for links (where one necessary condition is the same as a sufficient condition) and connect them. There's a bit of trial and error involved, but it seems to get faster with practice.

P1: A --> not B
B --> not A
P2: C --> B
not B --> not C
P3: not D --> A
not A --> D

You probably notice that there's a "not D" on the left side but never on the right side.
Let's put that on the far left:
not D --> A
Then you look for an A on the left side (P1) and add that to our chain:
not D --> A --> not B
Then you look for a "not B" at the left side (P2 contra) and add its necessary condition to the chain:
not D --> A --> not B --> not C
Then you notice that there are no "not C" statements on the left side. Looks like the chain is complete.
If necessary, we can take the contrapositive:
C --> B --> not A --> D
or use the original:
not D --> A --> not B --> not C

Hope that helps