None of the students taking literature are taking physics, but several of the students taking physics are taking art....

Naz on August 25, 2015

Let's diagram:

"None of the students taking literature are taking physics."

So: if you are student taking literature, then you are not taking physics.

P1: TL ==> not TP
TP ==> not TL

"but several of the students taking physics are taking art."

So: some of the students taking physics are also taking art.

Q1: TP-some-TA
TA-some-TP

"In addition, none of the students taking rhetoric are taking physics."

So: if you are a student taking rhetoric, then you are not taking physics.

P2: TR ==> not TP
TP ==> not TR

Answer choice (A) states: "There are students who are taking art but not literature."

So: some students who are taking art are not taking literature.

(A): TA-some-not TL
not TL-some-TA

Can we logically infer this from the statements above? Yes.

Remember we can combine a quantifier statement with a Sufficient & Necessary statement if the right-hand side variable of the quantifier statement is the same as the sufficient condition of the Sufficient & Necessary statement. We have that with P1 and Q1.

So, we can combine Q1 to P1 like so: TA-some-TP ==> not TL to infer: TA-some-not TL, which is answer choice (A).

Hope that clears things up! Please let us know if you have any other questions.