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  Logic
 
Shall We Dance? 		 
Q Does the third statement follow logically from the first two statements? Explain why or why not.

Statement 1:
All dancers are graceful.
Statement 2:
Some rocket scientists are graceful.
Statement 3:
Therefore, some rocket scientists are dancers.


 
A No, the third statement does not follow logically from the first two. If you replace the word "dancers" with the word "cats," and the words "rocket scientists" with the word "dogs," you will see more easily why not:

All cats are graceful.
Some dogs are graceful.
Some dogs are cats.

Even if the members of two groups share a common characteristics, it is still possible that none of the members of one group is also a member of the other.