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The 'who have never met' isn't the opposite of 'all know each other', it's no two people of these three know each other. The opposite would be don't all know each other.

If you imagine a six vertices arranged around a point and make any number of edges connecting them to represent knows each other. For any choice of edges, you can either find 3 vertices that are fully connected or you can find three vertices that have no connections.

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I would describe it as follows, maybe a little easier to visualize. Draw six dots, draw either a red or a blue line from every dot to every other dot. You must draw either a completely red triangle or a completely blue triangle. Personally I don't think it sounds intuitive when stated like that!

Thanks, personally I found this the easiest way to think about it!

Thanks, that clarifies it!

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