Treasure Island
In the middle of the ocean, there are two islands; one of the truth-telling tribe and one of the lying tribe. One day, you hear news of a secret treasure being buried on one of the islands and set sail to one of the islands with ambitious eyes. However, you do not know which island you have come to, and therefore ask one of the natives. The native says, "There exists treasure on this island if and only if I am telling the truth". Is there treasure on the island, and which tribe does this island belong to?
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2 solutions
Moderator note:
Yes. One needs to be careful when determining whether it's a conditional statement or a biconditional statement.
Worst case scenario, we can always construct a truth table.
Well done!
The sentence "There exists treasure on this island if and only if I am telling the truth." means: - if the treasure is here, be sure that we are truth-tellers - if we are truth-tellers, then the treasure is here In other words: "The treasure must be on the island of truth-tellers."
If he is a truth teller, the treasure is there. If he is a liar, then the treasure is not on the island of truth-tellers, so it's there again. Therefore, the treasure is there, but we do not know if he is a liar or the truth-teller.