Q. 104.2( 11 Votes )

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

Answer :

Onto function from the set {1, 2, 3, ..., n} to itself is simply a permutation on n symbols 1, 2, 3, …, n.

Therefore, the total number of onto maps from {1, 2, 3, …, n} to itself is the same as the total number of permutations on n symbols 1, 2, 3, …, n, which is n!

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PREVIOUSGiven a non-empty set X, consider the binary operation ∗: P(X) × P(X) → P(X) given by A ∗ B = A ∩ B ∀ A, B in P(X), where P(X) is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation ∗.NEXTLet S = {a, b, c} and T = {1, 2, 3}. Find F–1 of the following functions F from S to T, if it exists.F = {(a, 3), (b, 2), (c, 1)}

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