Question

Find the number of empty relation we can define on a non empty set A

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Answer 1

This is a question where you get tested for your ability to distinguish number of elements in an empty relation and number of empty relations. Clearly, the number of elements in an empty relation is zero, as no element is connected to any element. But the number of such relations is one, which is denoted by {}. We can define the same empty relation in different ways(using different phrasing and language), but they will all be equal to {}. So the number of empty relation we can define on a set is one.