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An elenchus is where a statement is made and then the truth of that statement is examined by calling upon other statements resulting from the first. If you wish to see examples then you would do well to read some of Plato's Socratic dialogues.
However, here is a simple example.
Person A: The world is not round, it is flat.
Person B: Do you agree that it is possible to travel in any direction and end up back at the same point you started from so long as you maintain that same direction?
Person A: Yes, that is true.
Person B: Would this be possible if the world was flat?
Person A: No.
Person B: Then we must agree that the world can not be flat.
Person A: Yes, you are right.
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