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Hey TLS.

I have trouble understanding the logic behind #18 in Section 2 of PT30.

"If there are any inspired musical performances in the concert, the audience will be treated to a good show. But there will not be a good show unless there are sophisticated listeners in the audience, and to be sophisticated listener one must understand one's musical roots."

Question: If all of the statements above are true, which one of the following must also be true?

Answer: (A) If there are no sophisticated listeners in the audience, there will be no inspired musical performance in the audience.

My understanding was that an inspired musical performance can occur whatever the audience, it is whether or not there will be a good show that the audience affects (i.e. if A (musical performance) then B (good show)). Am I making a mistake in translating this into formal logic form?

Will be greatly thankful for advice.

Inspired Musical Performances = IMP
SL = sophisticated listeners
GS = Good Show
UMR = Understand Musical Roots

Premise 1: IMP --> GS
Premise 2: ~SL --> ~GS
Premise 3: SL --> UMR

If you take the contrapositive of premise 2 you get GS --> SL which you can link to the first premise to get: IMP --> GS --> SL

A) says if you don't have SL (~SL) then you don't have IMP (~IMP) which is valid.

Taking the contrapositive of IMP --> GS --> SL is what yields answer choice A)

~SL --> ~GS --> ~IMP [don't have sophisticated listeners, then you don't have a good show, and consequently you don't have inspired musical performances.]

Thanks Cardozo, this makes sense. And +1 for proper notations