The lying bee and the truthful bee logic puzzle

There were two bees, Apollo and Buzz. Apollo said to Buzz, “I always tell the truth”. Buzz responded, “I always lie”.

One of these statements is correct. Which one?

Reveal solution

The statement by Buzz “I always lie” is an example of the liar paradox. If the statement were to be correct, it would contradict itself (Buzz cannot always lie if he tells the truth about always lying). Thus, given one of these statements was indicated to have been correct, it must be Apollo’s.