Find the number of all onto functions from th | vedclass

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(A) An onto function (surjective function) from a finite set $A$ to itself,where $|A| = n$,is a function where every element in the codomain has at le

Vedclass · Accepted Answer

$n!$

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(A) An onto function (surjective function) from a finite set $A$ to itself,where $|A| = n$,is a function where every element in the codomain has at least one pre-image in the domain.Since the domain and codomain have the same number of elements $(n)$,an onto function must also be injective (one-to-one).$A$ function that is both injective and surjective is called a bijection or a permutation.The total number of permutations of a set with $n$ elements is given by $n!$.Therefore,the total number of onto functions from the set $\{1, 2, 3, \ldots, n\}$ to itself is $n!$.

Find the number of all onto functions from the set $\{1, 2, 3, \ldots, n\}$ to itself.

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