Read the following statements and conclusions carefully. Assume that all statements are absolutely true, even if they contradict commonly known facts. Based solely on the statements, determine which of the conclusions logically follows.
Statements:
All paintings are art.
Some art is beautiful.
No beautiful thing is cheap.
All expensive things are beautiful.
Conclusions:
1. Some paintings are beautiful.
2. No painting is cheap.
3. Some art is not cheap.
4. All expensive things are not cheap.
Show answer & explanation
Correct answer: A
Explanation
Given Statements:
• All paintings are art.
• Some art is beautiful.
• No beautiful thing is cheap.
• All expensive things are beautiful.
Evaluating the Conclusions:
• Conclusion 1: Some paintings are beautiful. — Does not follow. All paintings are art and some art is beautiful, but the beautiful art may not include paintings.
• Conclusion 2: No painting is cheap. — Does not follow. There is no definite relationship established between paintings and cheap things.
• Conclusion 3: Some art is not cheap. — Follows. Since some art is beautiful and no beautiful thing is cheap, the part of art that is beautiful can never be cheap.
• Conclusion 4: All expensive things are not cheap. — Follows. All expensive things are beautiful, and since no beautiful thing is cheap, no expensive thing is cheap (all expensive things are not cheap).
Therefore, only (3) and (4) follow.