Some twentieth-century art is great art.
This means at least some (but not necessarily all) twentieth-century art is great.
All great art involves original ideas.
This means that if something is great art, it must have original ideas.
Any art that is not influential cannot be great art.
This means that all great art must be influential.
If art is great → It must be influential.
From these statements, we can deduce:
Great art → Original ideas + Influential.
Some twentieth-century art is great → So that art must have original ideas and be influential.
Evaluating Answer Choices:
We need to find the statement that does NOT logically follow from the given premises.
(A) Some influential art involves original ideas. (Follows logically)
We know that great art must have original ideas and be influential.
Since some twentieth-century art is great, this means some art is both influential and has original ideas.
Therefore, some influential art must involve original ideas.
(B) Some twentieth-century art involves original ideas. (Follows logically)
We know that some twentieth-century art is great.
All great art involves original ideas.
Therefore, some twentieth-century art must involve original ideas.
(C) Only art that involves original ideas is influential. (Does NOT follow logically - Correct Answer
We know that great art must be influential and have original ideas.
But this does NOT mean that all influential art must have original ideas.
Some art could be influential without being great, meaning it might not necessarily have original ideas.
This does not logically follow from the premises.
(D) Only art that is influential and involves original ideas is great art. (Follows logically)
We know that great art must be both influential and have original ideas.
This statement restates that great art must have those qualities.
(E) Some twentieth-century art is influential and involves original ideas. (Follows logically)
We already established that some twentieth-century art is great.
Great art must have original ideas and be influential.
So, some twentieth-century art must be influential and have original ideas.