What about: "The total cost is the square root of the quantity. Preposterous!" -> therefore there is no relationship between the quantity ordered and the tota

What about: "The total cost is the square root of the quantity. Preposterous!" -> therefore there is no relationship between the quantity ordered and the total cost? I don't see how this method proves which properties are related and which aren't. You can come up with ludicrous relationships between any two properties, but that doesn't mean there's no relationship at all.