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

Question

None of the students taking literature are taking physics, but several of the students taking physics are taking art. In addition, none of the students taking rhetoric are taking physics.

Which one of the following statements follows logically from the statements above? 
 
A. There are students who are taking art but not literature.

B. None of the students taking literature are taking art.

C. There are students who are taking rhetoric but not literature.

D. None of the students taking rhetoric are taking literature.

E. There are students who are taking both art and literature.

ElninoEffect · Answer

Students taking Literature: "L"
Students taking Physics: "P"
Students taking Arts: "A"
Students taking Rhetoric: "R"

L and P  are mutually exclusive events. i.e if L occurs P doesn't and vice versa.

There are students who are taking both  P and A.  (Overlapping set)

R and P  are again mutually exclusive events. i.e if R occurs P doesn't and vice versa.

A. There are students who are taking art but not literature.
 Yes, can be deduced. How.?
From the second statement, we know that there are people who are taking physics and arts both but these people are definitely not taking literature from statement one.

B. None of the students taking literature are taking art.
 We cannot deduce that. No such relationship has been provided.

C. There are students who are taking rhetoric but not literature.
 We cannot deduce that. No such relationship has been provided.

D. None of the students taking rhetoric are taking literature.
 We cannot deduce that. No such relationship has been provided.

E. There are students who are taking both art and literature.
 We cannot deduce that. No such relationship has been provided.

mavrck0102 · Answer

I feel like A,C and E can be logically inferred. Can an expert please shed light how A is the only correct answer

ryanstarr · Answer

It's because C and E only rise to the level of "may be true," whereas the standard for inference is "must be true." Answer A fits that: the art students who are also taking physics are definitely not taking literature (because physics and literature have zero overlap), so there are at least some students who are taking art but not literature. On the other hand, you can come up with scenarios to contradict C and E without breaking any of the conditions laid out in the prompt.

Answer C seeks to connect students taking literature to students taking rhetoric. The prompt says that nobody taking literature or rhetoric takes physics, but that's the only explicit connection that exists between the literature students and the rhetoric students. It's possible that all the students taking rhetoric also take literature (even if it seems unlikely). Maybe both are required courses for a certain degree, for instance. It's not really important to contextualize your counterscenario (though it  is  a lot of fun); the important thing is that the scenario doesn't violate the conditions.

Answer E benefits from the work done on A. There is a scenario that could counter E: if the several students taking art and physics are the  only  students taking art (they are, after all, the only art students mentioned), then none of the students taking art would be taking literature--they'd all be doing physics, and physics and literature don't overlap.

7Amulya · Answer

Hi Bunuel & Karishma,

Can you help me with the diagram for this question please. I am not able to figure out.

Regards,
Amulya

DmitryFarberMPrep · Answer

7Amulya

Start with the first and last statements, since they are conditionals and therefore simpler to diagram:

None of the students taking literature are taking physics 
 L -> ~P

None of the students taking rhetoric are taking physics 
 R -> ~P

Any conditional can also be rewritten as its contrapositive: just flip and negate.

P -> ~L
P -> ~R

Therefore, if someone is taking physics, they are taking neither literature nor rhetoric.

Now look at the middle statement:

Several of the students taking physics are taking art

Since this is a statement about some but not necessarily all cases, we can't say P -> A or A -> P in general. However, we can say "some P are A" or "some A are P." If some A are P, then the previous conditionals apply to them.

A (some)-> P -> ~L and ~R.

Some students taking art are taking neither literature nor rhetoric.

VerbalBot · Answer

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

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

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