The Island of Liars and Truth-Tellers

The Island of Liars and Truth-Tellers: You land on an island where inhabitants either always tell the truth or always lie. You meet two inhabitants: Zara and Mia. Zara says, "At least one of us is a liar." What are Zara and Mia?

Answer: Zara is a liar and Mia is a truth-teller. If Zara were a truth-teller, then her statement would mean Mia is a liar, but…