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

bcross May 31, 2020

Statement 3

Shouldn’t statement 3 be diagramed like I have it below? not I —> not great If not, why? I got the answer correct, but I clearly didn’t have the right reasoning? Also, I’m not following from the explanation how statements 2 and 3 can be combined.

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shunhe May 31, 2020

Hi @bcross,

Thanks for the question! So first of all, I think that your way of diagramming statement 3 is perfectly fine. Any art that is not influential cannot be great art. In other words, if it’s not influential art, it’s not great art, which is

~I —> ~G

just as you diagrammed.

Now as for why we can link sentences two and 3, note that we can take the contrapositive of statement 3 to get

G —> I

in other words, if art is great art, it’s influential art. Now, diagramming sentence 2, all great art involves original ideas. That basically means if it’s great art, it involves original ideas. So this can be diagrammed

G —> O

But now we know that if G, then O, and if G, then I. We can combine these to make one compound statement

G —> O & I

Now let’s take a look at (D), which tells us that only art that is influential and involves original ideas is great art. Remember we diagram X only if Y as X —> Y. So this gets diagrammed as

G —> O & I

which is exactly what we got from combining statements 2 and 3, and so (D) does follow logically from the set of statements. So I do think you had the right reasoning on top of the right answer, good job!

Hope this helps! Feel free to ask any other questions that you might have.