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Question -

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



Answer -

Suppose f is notone-one.

Then, there exists twoelements, say 1 and 2 in the domain whose image in the co-domain is same.

Also, the image of 3under f can be only one element.

Therefore, the rangeset can have at most two elements of the co-domain {1, 2, 3}

i.e f is not an onto function, a contradiction.

Hence, f must be one-one.

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