Gem thief

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Here is a liar/truth-teller puzzle I made up for an exam.


Detective Ruby Gould is investigating the theft of some rare gemstones. She has five suspects (named Al, Bob, Chris, Dan and Eliot). Each suspect either always lies or always tells the truth. Using the statements below, find the thief. Can you also determine which suspects are liars and which always tell the truth?

Al: “Bob or Chris stole the gems.”
Bob: “That’s false! It was either Chris or Dan.”
Chris: “I agree, Al is a liar.”
Dan: “Only one of us is truthful.”
Eliot: “The thief always tells the truth.”