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?

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Hint

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

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Answer

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

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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.