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Let A and B be two sets, with | A | = m, | B |...

Let A and B be two sets, with | A | = m, | B | = n, Then how many distinct surjection from A to B?

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Answer #1

Solurtion:-

  • Let X and Y be finite non-empty sets, with m and n elements both not equal to zero, respectively.

    Then the number of functions can be defined from X to Y is

    If then the number of injective functions from X to Y is

    If then the number of surjective functions from X to Y is

    If then the number of surjective functions from X to Y is zero.

    If m=n then the number of bijective functions from X to Y is n!

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