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

Ashley on August 16, 2015

Break down

Could you please break this question down, thank you

Melody 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.