Find thenumber of all onto functions from the set 1- 2- 3- hellip- - n-to itself-

Ontofunctions from the set 1, 2, 3, hellip; ,n to itself issimply a permutation on n symbols 1, 2, hellip;, n.Thus, thetotal number of onto maps from 1, 2 ...

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Find thenumber of all onto functions from the set {1, 2, 3, … , n)to itself.

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Solution

Ontofunctions from the set {1, 2, 3, … ,n} to itself issimply a permutation on n symbols 1, 2, …, n.
Thus, thetotal number of onto maps from {1, 2, … , n} to itselfis the same as the total number of permutations on n symbols1, 2, …, n, which is n.

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Find thenumber of all onto functions from the set {1, 2, 3, … , n)to itself.

Ontofunctions from the set {1, 2, 3, … ,n} to itself issimply a permutation on n symbols 1, 2, …, n.Thus, thetotal number of onto maps from {1, 2, … , n} to itselfis the same as the total number of permutations on n symbols1, 2, …, n, which is n.

Ontofunctions from the set {1, 2, 3, … ,n} to itself issimply a permutation on n symbols 1, 2, …, n.
Thus, thetotal number of onto maps from {1, 2, … , n} to itselfis the same as the total number of permutations on n symbols1, 2, …, n, which is n.