Some students attending a small university with a well-known choir live off campus. From the fact that all music majo...

ankita96 June 22, 2020

Ans Choice A

I still do not understand how A is correct, especially with the first quantifier statement that "some students are in the choir and live off campus." Could you please elaborate on this and all point out why other answer choices are wrong. Thank You!!

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shunhe June 23, 2020

Hi @ankita96,

Thanks for the question! So the first quantifier statement actually isn’t super relevant to actually getting to the answer. What really matters is that all music majors are members of the choir. In other words

Music major —> Member of the choir

Now, a professor concludes that none of the students who live off campus are music majors; in other words, if you live off campus, you’re not a music major. We can diagram this as

Live off campus —> ~Music major

OK, well now we need to assume one of the answer choices to get to the conclusion. And clearly, it’s going to have to be something that links the idea of being a music major or being a member of the choir with living off campus. Take a look at (A), which tells us that none of the students who live off campus is a member of the choir; in other words, if you live off campus, you’re not a member of the choir. This means

Live off campus —> ~Member of the choir

And from the contrapositive of the “all music majors” sentence we know that

~Member of the choir —> ~Music major

And so we can get

Live off campus —> ~Member of the choir —> ~Music major

Which by the transitive property means

Live off campus —> ~Music major

Which is what the professor concludes. So if we assume (A), we can get to the conclusion, and so (A) is the correct answer choice here.

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ankita96 June 29, 2020

Hi,
Yes i do look at those explanations, however i wasn't sure how the first line was irrelevant , thus posted here.

Thank you!!