Imagine there are 3 coins on the table: gold, silver, and copper. If you make a truthful statement, you will get one coin. If you make a false statement, you will get nothing.
What sentence can guarantee you getting the gold coin?
You will have to say, “You will give me neither copper nor silver coin.”
If it is true, then you will get the gold coin. If it is a lie, then the negation must be true, so the statement becomes: “You will give me either copper or silver coin”. This would break the given conditions that you get no coin when lying. So the first sentence must be true.