#22 - Paulsville and Longtown cannot both be included in the

[Administrator]

Complete Question Explanation

Parallel Reasoning. The correct answer choice is (B).

Answer choice (A):

Answer choice (B): This is the correct answer choice.

Answer choice (C):

Answer choice (D):

Answer choice (E):

This explanation is still in progress. Please post any questions below!

[Megan Rogers]

Hey, I have a question regarding Q13. (from June 1994, LR 2, #22)

According to the stimulus, I came up with a diagram like this:

P or L (not both)
~P S
~S P ~L

and I drew (B)'s diagram as follows:

P or C (not both)
~M P
~M P ~C

I thought that (B) was not the correct answer because I thought that the last part of the diagram should have been the contrapositive form of the first sentence
(~P M ...) instead of starting with ~M.

Can someone help me with this question please?

Thanks in advance!

[Emily Haney-Caron]

Hi Megan,

Here's how I diagrammed this one:
Rules:
P L
~P S
~S P

Conclusion:
~S P ~L


B:
Rules:
P C
~M P

Conclusion:
~M ~C (implied: ~M P ~C)

B is the right answer here because the rules generally set up the same relationships, and the conclusions are paralleled. You're right that the two are not identical; however, with this type of question, you're looking for the answer choice that has reasoning closest to the stimulus; B is definitely closer than any of the other answers.

[PositiveThinker]

The reasoning i saw in the stimulus was . "P and L cannot both be on the itinerary" Which is basically P---> /L .. your standard not both conditional statement.
The stimulus goes onto say that P---->S. And that S did not happen so they went to L.
The logic basically just negates the necessary/ takes the contrapositive of the P---->S condition to then tell you L is not going to stopped at.

Does that mean P and L are a not both Bi-conditional?

It looks like answer choice B simply satisfies necessary. Whereas the stimulus negated necessary.
Answer choice C looks like it negates the necessary the same way that the stimulus does. If i can get some feed back on this that would be great.

[Kristina Moen]

Hey there PositiveThinker,

You wrote: "The stimulus goes onto say that P---->S"

Careful with the conditional statement that uses the word "unless." Remember that there's a special rule for how to treat the word "unless." You take the part being modified by "Unless" (here that's "Salisbury is made part of the itinerary") and that becomes the necessary condition. The other part is the sufficient condition - but you have to negate it. So "The candidate will make a stop in Paulsville" becomes "The candidate will not make a stop in Paulsville." So this becomes NO Paulsville Salisbury. By the way, you do the the same thing if you see the word "until," "except," and "without."

So what you have here is:
Premise 1: P L
Premise 2: NO P S
Premise 3: NO S.
Conclusion: NO L.

This is done by taking the contrapositive of Premise 2. If no S, then the candidate MUST stop in P. And you can't have both P and L! So no L.

Now take a look at answer choices (B) and (C)!

[PositiveThinker]

Hey there PositiveThinker,

You wrote: "The stimulus goes onto say that P---->S"

Careful with the conditional statement that uses the word "unless." Remember that there's a special rule for how to treat the word "unless." You take the part being modified by "Unless" (here that's "Salisbury is made part of the itinerary") and that becomes the necessary condition. The other part is the sufficient condition - but you have to negate it. So "The candidate will make a stop in Paulsville" becomes "The candidate will not make a stop in Paulsville." So this becomes NO Paulsville Salisbury. By the way, you do the the same thing if you see the word "until," "except," and "without."

So what you have here is:
Premise 1: P L
Premise 2: NO P S
Premise 3: NO S.
Conclusion: NO L.

This is done by taking the contrapositive of Premise 2. If no S, then the candidate MUST stop in P. And you can't have both P and L! So no L.

Now take a look at answer choices (B) and (C)!

I made an amateur mistake! yikes. Im usually pretty good at conditional logic. I just didn't look closely enough at the stimulus to see the "unless."
Thank you!

[gmosquera42]

Can you please explain why B is correct?

When diagrammed I get the below:

P M
Not P C
Not M
Not C

[James Finch]

Hi Gmosquera,

(B) switches up the order in which the premises are given, which may have thrown you off. Whichever way the order is given, however, the logic in (B) is the same as in the stimulus. Let's break it down:

First, we are told M P, then P C, and finally M C

This answer choice then ends up having the same A B C, thus A C reasoning as in the stimulus, making it correct.

Hope this helps!

[flowskiferda]

Why can't I say:
S no P and the contrapositive P no S?
When it says the candidate will make a stop in Paulsville unless Salisbury is on the itinerary, doesn't that mean that Salisbury's presence would guarantee no stop in Paulsville (S no P)?

[Jeremy Press]

Hi flow,

The nature of "unless" statements prevents you from diagramming that way. There's both a formulaic and a more "intuitive" way of thinking about the logic of unless statements. The formulaic way of thinking about them (if you memorize it) will ensure you never inaccurately diagram "unless" statements.

Here's the formulaic way to think about it, using what PowerScore calls the Unless Equation.

The first step of the Unless Equation is to diagram the part of the statement modified by unless as the necessary condition. Here, Salisbury being part of the itinerary is modified by unless, so it becomes the necessary condition (on the right side of the arrow), per below:

S

The second step of the Unless Equation is to negate (i.e., state the logical opposite of) the remaining condition, then diagram it on the sufficient side of the arrow. Here, the remaining condition is "[t]he candidate will make a stop in Paulsville," so we need to negate that to "[t]he candidate will NOT make a stop in Paulsville" then diagram that on the sufficient side of the arrow, per below:

P S

The intuitive reason this diagramming procedure is required is because of the nature of "unless" statements, which are speaking about exceptions to a normal situation. In this case the normal situation is that the candidate will make a stop in Paulsville. The exception to that (the necessary circumstance in which the candidate will NOT make a stop in Paulsville) is when Salisbury is part of the itinerary. In other words, if the exception (the candidate NOT making a stop in Paulsville) is going to occur, then it MUST be the case that Salisbury is on the itinerary. Since the unless statement speaks to that exception (candidate NOT making a stop in Paulsville) our diagram has to reflect that, and it has to reflect that what is necessary for that exception to occur is the "unless" condition (Salisbury being on the itinerary). Hence, the Unless Equation above, which gets us to the right logical diagram!

I hope this helps!