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

Naz on January 3, 2014

Let's diagram the stimulus:

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

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

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

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

"A stop in Salisbury is out of the question."

P: not S

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

C: not L

Let's see if this is a valid argument. We can take the contrapositive of the second premise: not S ==> P and connect it to the principle rule of the first premise: P ==> not L like so: not S ==> P ==> not L, to conclude through the transitive property: not S ==> not L. Therefore, we have a valid transitive argument.

Answer choice (C) is not correct because it does not closely parallel the stimulus. Let's diagram answer choice (C)

"The program committee never selects two plays by Shaw for a single season."

This means that the program committee can select max one S in a single season.

"But when they select a play by Coward, they do not select any play by Shaw at all."

P: C ==> not S
S ==> not C

"For this season, the committee has just selected a play by Shaw,"

P: S

"So they will not select any play by Coward."

C: not C

Though this is a valid argument, it does not parallel that in the stimulus. Not only is the structure of the argument not similar, but we also do not use the transitive property to arrive at our conclusion. Rather it is just the contrapositive of the second premise that is being invoked (i.e. S ==> not C).

Hope that helped! Please let us know if you have any more questions.