Fundamentals of Mathematical Logic

Question

You meet three inhabitants of Davison's Island and have the following talk. Can you tell which inhabitants (if any) are lying?

A says, “Exactly one of us is telling the truth.”

B says, “We are all lying.”

C says, “The other two are lying.”

Answer 1

Well obviously B must be lying. If B is telling the truth, then all three are lying, which can't be true.

So if B is lying, someone must be telling the truth (A or C or both).

If C is telling the truth, then A and B are lying, but what A says is true, so C must be lying.

If A is lying, then all 3 are lying, which means that B must be truthful which isnt true

So A tells the truth, B and C are lying