how many relations are possible from a set a of m, Mathematics

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how many relations are possible from a set a of m

How many relations are possible from a set A of 'm' elements to another set B of 'n' elements?

Ans: A relation R from a set A to other set B is specified as any subset of A x B. If |A| = m and |B| = n, after that |A x B| =mn and thus number of possible subsets of A x B = 2^mn. Every subset is a relation from A to B. So there are 2^mn dissimilar types of relations from A to B.

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