Paulsville and Longtown cannot both be included in the candidate's itinerary of campaign stops. The candidate will ma...

Mehran on August 14, 2013

Let's break down the argument...

Principle #1:
"Paulsville and Longtown cannot both be included."

P ==> not L
L ==> not P

Principle #2:
"The candidate will make a stop in Paulsville unless Salisbury is made part of the itinerary."

not P ==> S
not S ==> P

Premise:
"Unfortunately, a stop in Salisbury is out of the question."

not S

Conclusion:
"Clearly, then, a stop in Longtown can be ruled out."

not L

We know from Principle #2 that if "not S" then "P." We also know from Principle #1 that if "P" then "not L." So this is a valid transitive argument.

not S ==> P ==> not L

Let's take a look at the answer choices (A) and (B):

(A) is an invalid argument. The premise "not S" is sufficient to conclude "not R" but "not R" does not lead to anything else.

PR: R ==> not GP
GP ==> not R

PR: R ==> S
not S ==> not R

P: not S
C: not GP

(B) is correct because it exactly parallels the argument.

PR: not M ==> P
not P ==> M

PR: P ==> not C
C ==> not P

P: not M
C: not C

This is a valid transitive argument.

not M ==> P ==> not C

Hope this helps! Please let us know if you have any other questions.

erojas on February 9, 2018

I'm not seeing that all of the logic was written out in answer choice B. Where are you showing: "and Tom will not support both Parker and Chung"? I just want to make sure I am following the argument correctly.

Mehran on February 9, 2018

Hey @erojas, thanks for your post. Great question. "and Tom will not support both Parker and Chung" is diagrammed in our previous post as P - > not C (contrapositive C - > not P). If Tom supports P, he won't support C. If Tom supports C, he won't support P. Hope this helps!

LH44 on March 17, 2019

Hello, in the question, we use the contrapositive of the second Principal Rule (not S==>P) and the transitive property to come to the conclusion. In the answer choice B, we use the Transitive property but not the contrapositive of one of the Principal Rules. On the LSAT, if I came to B and saw it was valid, should I keep looking at C,D and E to see if one of them used both the transitive property and the contrapositive of a Principal Rule or could I be comfortable selecting B and moving on? Hope that makes sense, thanks!

hannahnaylor5 on August 24, 2019

I had the same question as the one above. I ruled out B because it did not invoke the contrapositive of any premise, as did the argument in the stimulus. This time it was okay that they didn't match but other times it's not so I'm confused?

Hannah-Anderson on August 27, 2019

I'm wondering about the same questions as the two posts above? Am I missing a parallel between the question and the correct answer where the contrapositive was invoked in this instance? Or, is this one question where you have to rule out all other choices and in this case the "most closely parallels" answer is one that doesn't quite precisely parallel the prompt? Just hoping for some clarification here.

Irina on August 27, 2019

@Hannah-Anderson & @hannahnaylor5,

The stimulus and (B) can actually be diagrammed exactly the same way:

P & L cannot both be included in the itinerary:

(1) ~(p & l)

per De Morgan's Law, this is logically equivalent to:

(2) ~ p v ~l

The candidate will stop in P unless S is part of the itinerary:

(3) ~s-> p

S is out of the question:

(4) ~s

using modus ponens rule, we can infer per (3):

(5) p
___________
Clearly, L can be ruled out:

~l

This conclusion requires to use the rule of inference known as disjunctive syllogism to infer that:
~ p v ~ l (2)
p (5)
~l

Now, let's compare it to (B)

Tom will not support both P & C

(1) ~ p v ~c

Tom will definitely support P if M does not apply

(2) ~ m ->p

M does not apply

(3) ~m

we can infer per (2):

p
___________
Clearly, C will not get T support.

~c

This conclusion again requires us to use disjunctive syllogism:

~ p v ~ c (1)
p (4)
~ c


The bottom line here, there are multiple ways to accurate diagram the logic in these arguments. If you are comfortable with the rules of inference, you could pick (B) and move on. If you cannot right away determine that the arguments are the same, you could reach the correct answer by process of elimination. I would not rule out an answer choice just because it uses a slightly different set of rules of inference to reach the same conclusion.

Let me know if this helps and if you have any other questions.

Amanda_r01 on May 7, 2020

Sorry if I repeat any previous thoughts, I honestly did not read all the comments.
I have this simple question, so basically we are basing the right answer in the structure of the reasoning leading to both being "valid transitive arguments"?

BenMingov on May 7, 2020

Hi Amanda, no worries at all!

Yes, and they both follow the same structure of sufficient necessary statements.

In the passage:

Not S -> P -> Not L

In the answer choice

Not M -> P -> Not C

I hope this helps. Please let me know if you have any other questions or would like me to elaborate further.