2000 AMC 10 Problems/Problem 21
Problem
If all alligators are ferocious creatures and some creepy crawlers are alligators, which statement(s) must be true?
Solution
We interpret the problem statement as a query about three abstract concepts denoted as "alligators", "creepy crawlers" and "ferocious creatures". In answering the question, we may NOT refer to reality -- for example to the fact that alligators do exist.
To make more clear that we are not using anything outside the problem statement, let's rename the three concepts as , , and .
We got the following information:
- If is an , then is an .
- There is some that is a and at the same time an .
We CAN NOT conclude that the first statement is true. For example, the situation "Johnny and Freddy are s, but only Johnny is a " meets both conditions, but the first statement is false.
We CAN conclude that the second statement is true. We know that there is some that is a and at the same time an . Pick one such and call it Bobby. Additionally, we know that if is an , then is an . Bobby is an , therefore Bobby is an . And this is enough to prove the second statement -- Bobby is an that is also a .
We CAN NOT conclude that the third statement is true. For example, consider the situation when , and are equivalent (represent the same set of objects). In such case both conditions are satisfied, but the third statement is false.
Therefore the answer is .
See Also
2000 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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