If A = 1, 2, 3 , show that a onto function f : A → A must be one-… - Vidyadip

Question

If A = {1, 2, 3}, show that a onto function f : A → A must be one-one.

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Answer

A = {1, 2, 3}
Possible onto function from A to A can be the following:

{(1, 1), (2, 2), (3, 3)}
{(1, 1), (2, 3), (3, 2)}
{(1, 2), (2, 2), (3, 3)}
{(1, 2), (2, 1), (3, 3)}
{(1, 3), (2, 2), (3, 1)}
{(1, 3), (2, 1), (3, 2)}

Here, in each function, different elements of the domain have different images.
Therefore, all the function are one-one.

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