For some reason i'm having trouble with this problem...:o

Prove that a mapping is one-to-one iff for every pair of subsets and of .

we define something like by

Thanks guys

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- Jan 31st 2008, 10:41 PMJhevonMapping Proof
For some reason i'm having trouble with this problem...:o

Prove that a mapping is one-to-one iff for every pair of subsets and of .

we define something like by

Thanks guys - Feb 1st 2008, 12:21 AMbadgerigar
a mapping is one-to-one if for every pair of subsets A and B of S.

The contrapositive of this is:

if for every pair of subsets A and B of S then is not one to one.

intuitively,

So implies that there is some element in that is not in . So there is an element a in A and an element b in B such that but so so is not one-to-one.

To go the other way, we know that the function is not one-to-one so for some . using A={a} and B = {b}, .