Question:

The number of bijective functions from the set $A$ to itself, if $A$ contains $108$ elements is -

Updated On: May 11, 2024
  • $180$
  • $(180)!$
  • $(108)^!$
  • $2^{108}$
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The Correct Option is C

Solution and Explanation

Since number of one-one onto functions from a set A having n elements to itself is n!.
We have the set A that contains 108 elements, so the number of bijective functions from set A to itself is 108!
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Concepts Used:

Relations and functions

A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.

A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.

Representation of Relation and Function

Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.

  1. Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
  2. Roster form - {(1, 1), (2, 4), (3, 9)}
  3. Arrow Representation