Technically, after the "either" you should have parallel structure, which 2 and 3 have, but 1 does not. Practically, my "ears" stumble a little over 2, and in 2, the phrase true or false is so ingrained in our brains that it doesn't sound wrong. Spoken, I'd go with either 1 or 3; in writing, I'd use 3, because people who check for parallelism will find it missing in 1 and in my opinion, simpler is better (and 3 is simpler than 2).
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