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Provide solution for RD Sharma maths class12 Chapter Functions exercise 2.1  question 16

Answers (1)

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Given:

Here given that \left \{ 1,2,3....n \right \}  is the set.

Here we have find all onto function from the given set.

Hint:

Since if f is onto then all element have a unique pre image.

Solution:

Taking the set \left \{ 1,2,3 \right \}

\therefore Total number of one-one function 3\times 2\times 1=6

As example since f is onto, all elements of \left \{ 1,2,3 \right \} have unique pre-image

Element Number of possible pairs
1 3
2 2
3 1

So as the diagram, we get

Elements Number of possible pairs
1 n
2 n-1
3 n-2
. .
. .
n-1 .
n 2
  1

So as the diagram, we get n \times(n-1) \times(n-2) \times \ldots \times 2 \times 1=n !

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