## No-data one year ago 1. How many distinct binary relations can be constructed from a given set A with cardinality 3 to a given set B with cardinality 4?

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I think I can construct 3 * 4 + 1 distinct binary relations.

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I think I was lost. To know the number of binary relations I can get from to given set with known cardinalities I need to know the cardinality of the power set of the cartesian product. I know that the cardinality of a power set is given by:$\#P(A) = 2^{\#A}$

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And I know too that the cardinality of the Cartesian product is equal to the product of the cardinalities of every set involved. So $\#(A\times B) = \#A\cdot \#B$

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So $\#P(A\times B)=2^{\#A\cdot \#B}$

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So the number of binary relations I cant get is given by: $2^{12}$

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Is it right?