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Show that a one-one function f : {1, 2, ...

Show that a one-one function `f : {1, 2, 3}-> {1, 2, 3}`must be onto.

Text Solution

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A function `f: A -> B` is called an onto function if the range of f is `B`.
In other words, if each `b in B` there exists at least one `a in A` such that
`f(a) = b`, then f is an on-to function.

Here, `f: {1,2,3} ->{1,2,3}`
Here, `A = {1,2,3}`
`B = {1,2,3}`
Here, as given function is one-one and for each value of `B`, there exists a value in `A`,
...
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