Three people called Alf, Beth, and Gemma, sit together in the same room.

One of them always tells the truth.

One of them always tells a lie.

The other one tells truth or lies at random.

In each of the following situations, your task is determine how each person acts.

Suppose that Alf says “I always tell lies” and Beth says “Yes, that’s true, Alf always tells lies”.

Who always tells the truth? Who always lies? Briefly explain your answer.

Suppose instead that Gemma says “Beth always tells the truth” and Beth says “That’s wrong.”

Who always tells the truth? Who always lies? Briefly explain your answer.

Suppose instead that Alf says “Beth is the one who behaves randomly” and Gemma says “Alf always lies”. Then Beth says “You have heard enough to determine who always tells the truth”.

Who always tells the truth? Who always lies? Briefly explain your answer.