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Let A be a finite set. If f: A->A is a o...

Let `A` be a finite set. If `f: A->A` is a one-one function, show that `f` is onto also.

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Let `A={a_1, a_2. .....a_n}`
Since `f` is one -one.
`f(a_1), f(a_2)...f(a_n)` is distinct element of `A`.
`A={f(a_1), f(a_2)...f(a_n)}`
Let `b` be any element of `A`. Then `b=f(a_i)` for some `i`, `1<-i<-n`.
`:. f` is onto
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