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  • 3 years 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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  1. No-data
    • 3 years ago
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    I think I can construct 3 * 4 + 1 distinct binary relations.

  2. No-data
    • 3 years ago
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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:\[\#P(A) = 2^{\#A}\]

  3. No-data
    • 3 years ago
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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 \[\#(A\times B) = \#A\cdot \#B\]

  4. No-data
    • 3 years ago
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    So \[\#P(A\times B)=2^{\#A\cdot \#B}\]

  5. No-data
    • 3 years ago
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    So the number of binary relations I cant get is given by: \[ 2^{12} \]

  6. No-data
    • 3 years ago
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    Is it right?

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