A set of propositions is listed. Draw a Venn diagram that represents all the information in the propositions and use it (and no other assumptions) to answer the question. Explain your reasoning.No dogs are cats. No gerbils are cats. All dogs have fleas. Some cats are thirsty. No thirsty creatures have fleas.Question: Could a gerbil be a dog?

Question

What will be an ideal response?

Answer 1

Answers may vary. One possibility:

Yes, a gerbil could be a dog. We know from the first proposition that the set "dogs" is disjoint from the set "cats," and we know from the second proposition that the set "gerbils" is disjoint from the set "cats." However, we do not know the relationship between the sets "dogs" and "gerbils." It is possible that the two sets are not disjoint; if so, they will overlap in region a. A gerbil who is a dog would necessarily have fleas, since all dogs have fleas. Such a gerbil would not be thirsty, since no thirsty creatures have fleas.