Who does which?

There are three people, Demarcus, Eli and Dominic. One is a farmer, one is a salesman and one is a debt collector, but you don't know who does which. You ask them about their job and get the following answers:

• Demarcus: Eli is not a debt collector and Dominic is a salesman.
• Eli: Demarcus is a farmer and Dominic is not a debt collector.
• Dominic: Eli is not a salesman and Demarcus is a debt collector.

A friend of yours who had listened to the conversation tells you: "Actually, only one of them told the truth". Which is the job of each of them?

Hint

Think about boolean algebra and proceed with the method of proof by contradiction.

Answer

Dominic is a farmer, Eli is a debt collector and Dominic is a salesman.

Solution

Let's assume that Demarcus told the truth. Then Dominic is a salesman and Demarcus is a debt collector. But then Dominic also told the truth. That's a contradiction. Let's assume that Dominic told the truth. Then Demarcus is a debt collector and Dominic is a salesman. But then Demarcus also told the truth. Another contradiction. So, the one who told the truth is Eli. Then, Demarcus is a farmer, Eli is a debt collector and Dominic is a salesman.