In West Calverton, most pet stores sell exotic birds, and most of those that sell exotic birds also sell tropical fis...

Antionette on January 21, 2014

Help

Please explain how to diagram.

3 Replies

Melody on January 22, 2014

Let's diagram:

"In West Calverton, most pet stores sell exotic birds,"

Q1: PS-most-SEB
SEB-some-PS

"and most of those that sell exotic birds also sell tropical fish."

Q2: SEB-most-STF
STF-some-SEB

"Any pet store there that sells tropical fish, but not exotic birds does sell gerbils."

P1: STF & not SEB ==> SG
not SG ==> not STF or SEB

"No independently owned pet stores in West Calverton sell gerbils."

P2: IOPS ==> not SG
SG ==> not IOPS

Answer choice (D): "No independently owned pet store in West Calverton sells tropical fish but not exotic birds."

IOPS ==> not STF or SEB
STF & not SEB ==> not IOPS

Answer choice (D) follows from connecting P2 to P1's contrapositive:

IOPS ==> not SG ==> not STF or SEB, to conclude:

IOPS ==> not STF or SEB

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

Missy on November 2, 2015

I understand why the correct answer is D but can you explain why E is incorrect.

Mehran on November 9, 2015

Thank you for your question.

None of the statements we can diagram as joint sufficient conditions (1) the quality of being independently owned and (2) the quality of not selling tropical fish. Nor are these conditions found jointly in the contrapositive form, that is, (1) the quality of not being independently owned or (2) the quality of selling tropical fish. That is why (E) is incorrect: there is no textual support in the stimulus for the proposition that IOPS & STF ==> SEB.

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