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If function f(x) is defined from set A t...

If function f(x) is defined from set A to B, such that `n(A)=3` and `n(B)=5`. Then find the number of one-one functions and number of onto functions that can be formed.

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To solve the problem, we need to find the number of one-one (injective) functions and onto (surjective) functions from set A to set B, given that \( n(A) = 3 \) and \( n(B) = 5 \). ### Step 1: Finding the number of one-one functions A one-one function means that each element in set A maps to a unique element in set B. Since \( n(A) = 3 \) and \( n(B) = 5 \), we can select 3 elements from set B for the 3 elements in set A. 1. The first element from set A can be mapped to any of the 5 elements in set B. 2. The second element from set A can then be mapped to any of the remaining 4 elements in set B. ...
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Knowledge Check

  • If A and B are two sets such that n(A)=5 and n(B) = 6, then the number of one-one and onto mapping from A to B is

    A
    120
    B
    720
    C
    0
    D
    none of these

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