Some twentieth-century art is great art. All great art involves original ideas, and any art that is not influential ...

Naz May 4, 2015

Let's diagram the set of statements.

"Some twentieth-century art is great art."

P1: 20thA-some-GA
GA-some-20thA

"All great art involves original ideas."

P2: GA ==> IOI
not IOI ==> not GA

"any art that is not influential cannot be great art."

P3: not IA ==> not GA
GA ==> IA

Now let's look at the answer choices.

(A): "Some influential art involves original ideas."

(A): IA-some-IOI
IOI-some-IA

Well we know from P2 that "GA ==> IOI" and we know from the contrapositive of P3 that "GA ==> IA." Whenever the sufficient conditions of two Sufficient & Necessary statements are the same, we can combine their necessary conditions into a some statement like so: IOI-some-IA, which is answer choice (A). Thus, answer choice (A) can be logically concluded from the set of statements.

(D): "Only art that is influential and involves original ideas is great art."

(D): GA ==> IA and IOI
not IA or not IOI ==> not GA

Well, we know from P2 that "GA ==> IOI," and we know from the contrapositive of P3 that "GA ==> IA." Thus, all "GA will have "IOI" and "IA," which is what answer choice (D) states, since we know that the word "only" introduces a necessary condition. Do not mistake this statement to mean that the only type of great art is that which is influential and involves original ideas, because that is a wholly different statement. Therefore, answer choice (D) can be logically concluded from the set of statements.

(E): "Some twentieth-century art is influential and involves original ideas."

(E) 20thA-some-IA
IA-some-20thA

20thA-some-IOI
IOI-some-20thA

The "and" in the necessary condition acts as a conjunction joining two separate thoughts together, meaning we can separate each one into its own necessary condition. For example, if you has A ==> B & C, you could split that into A ==> B and A ==> C.

Now, we can connect P1 to P2, like so: 20thA-some-GA ==> IOI to conclude: 20thA-some-IOI. We can also connect P1 to the contrapositive of P3 like so: 20thA-some-GA ==> IA to conclude: 20thA-some-IA. Thus, answer choice (E) can also be logically concluded from the statements above.

Hope that was helpful! Please let us know if you have any other questions.

Richard May 6, 2015

It is awesome clear. Thanks!

yababio May 21, 2015

Like i said before i dont want to read a paragraph wheres the video

Naz May 21, 2015

There is no need for a video explanation to this question since it has no major visual components. Please refer to the written explanation above for a breakdown of the problem.

Hope that helps! Please let us know if you have any other questions.

awashing November 10, 2016

I don't see the corresponding explanations for choice (B) and (C) above. Could you please add? Also it would be much easier to read the long parenthetical explanations if there was some way to distinguish, either by underlining or bolding, the explanation for each answer choice.

Alex January 4, 2017

Hello, how does C set up? I -> AIOI, Not AIOI -> Not I. The passage does not mention influential but influential art? Is that the reasoning that it does not follow logically? Thank you.

Mehran January 15, 2017

@Alex we know "only" introduces a necessary condition so (C) would be diagrammed as follows:

I ==> AOI
not AOI ==> not I

From the stimulus, we know the following:

"Some twentieth-century art is great art."

20thCA-some-GA
GA-some-20thCA

"All great art involves original ideas . . . "

GA ==> OI
not OI ==> not GA

"any art that is not influential cannot be great art."

not IA ==> not GA
GA ==> IA

So while the passage does in fact mention influential art, (C) does not follow logically from the information in the stimulus.

Hope this helps! Please let us know if you have any other questions.

Marie November 19, 2017

thanks that was helpful!