Problem 43: Alien Encounter

I saw this problem on another blog page. It is from Steven Strogatz's famous book Professor Stewart's Cabinet of Mathematical Curiosities. I like such Knights and Knaves type of logical reasoning questions. I use them a lot while teaching "Logic" in IB DP Math Studies course.

Here is the question:

 

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Solutions to such questions need seeing the big picture of the case, and often students struggle doing this. That's why I prefer them drawing diagrams or truth table-like charts. 

Sometimes a tree diagram from probability unit is helpful.
So let's try a solution using tree diagrams.

Assume that Alfy tells the truth. Therefore he must be a Veracitor. What he tells about Betty is also true. So Betty is Gibberish. Betty says Alfy and Gemma are same species but she is lying. Therefore Gemma must be Gibberish. This coincides with Gemma saying Betty is Veracitor, which she is not. So Gemma is a liar and it matches with what we found from Alfy and Betty's answers. So our answer is Alfy: Veracitor; Betty and Gemma: Gibberish.

It is better to see the other option where Alfy is dishonest. This time we see that, if he is a liar, then Betty must be a Veracitor. If Betty is Veracitor, then Gemma must be Gibberish since Betty is honest in this option. However being a Gibberish, Gemma must be a liar. However, Gemma says Betty to be a Veracitor which is true. This truth creates a contradiction. Therefore this option is not reasonable at all and Alfy must be telling the truth. So the answer is the previous one.