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Show that an onto function f : {1, 2, 3}...

Show that an onto function `f : {1, 2, 3} ->{1, 2, 3}`is always one-one.

Text Solution

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Let `f` is not one-one.
Then, at least two elements will have the same image.
If `1` and `2` have same image `1` and `3` has the image `3`,
then `2` has no pre-image.
Hence, `f` is not onto.
But, we are given `f` is an onto function which means our assumption is incorrect.
`:.` f is one-one function.
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