Please help me with this, I'm not sure I understand it and don't know where to start

Let A and B be finite sets with |A| = |B|. Suppose thatf: A--->B. Prove thatfis injective if and only iffis surjective

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- Sep 20th 2009, 02:06 PMDaxHelp with injective, surjective proof
Please help me with this, I'm not sure I understand it and don't know where to start

Let A and B be finite sets with |A| = |B|. Suppose that*f*: A--->B. Prove that*f*is injective if and only if*f*is surjective - Sep 20th 2009, 02:29 PMPlato
- Sep 20th 2009, 03:32 PMDax
is there an easier way to explain that, none of that looks familiar, i'm only a few weeks into the class and that doesn't make sense to me at all

- Sep 20th 2009, 04:07 PMPlato
Look, this is not a trivial problem. It usually makes use of the pigeon-hole principle.

You are not going to find a trivial proof. Any proof is equivalent to proving a form of the pigeon-hole principle.

That said, try this.

Suppose that is injective.

is collection of pair-wise disjoint subsets of .

But by the nature if functions .

From that how can conclude that is surjective?