The number of relations that can be defined on a set A to A itself equals to the cardinality of the power set of the Cartesian product


The number of relations that can be defined on a set A to A itself equals to the cardinality of the power set of the Cartesian product

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The number of relations that can be defined on a set A to A itself equals to the cardinality of the power set of the Cartesian product of A, i.e., |P(AxA)| = 2^n^2  , where n^2 = |AxA|. For example, given a set A = {-1, 0, 1}, the number of relations defined on A to A is 2^9 = 512. Question: How many relations of the above contain the pair (0, 0)?


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