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CTK Exchange
Dad
guest
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May-31-08, 09:41 PM (EST) |
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"proof"
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Let A be a set and let D be the set of all bijections from A to itself. Define a relation ~ on D by f~g <==> ∃h∈ D such that h º f = g º h. Prove ~ is an equivalence relation |
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alexb
Charter Member
2231 posts |
May-31-08, 09:55 PM (EST) |
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1. "RE: proof"
In response to message #0
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Well, let's think. You have to show
- Reflexivity
If 1 is the identity mapping then fº1 = 1ºf.
- Symmetry
If there is an h s.t. fºh = hºg then since h is a bijection h-1 exists so that h-1ºf = gºh-1.
- Transitivity
In the same vein
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