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Unformatted text preview: (upon expanding) xxy =y x (1y ) =y x =y 1y = y y1 Now we return to the proof. ] Dene x = y y1 . Then x R as y R { 1 } . Also, x 6 = 1. [ To check this: Assume for a contradiction that x = 1 . Then x = y y1 = 1 y = y1 0 =1 , a contradiction. ] Thus x R { 1 } , the domain of f . We then have that f ( x ) = f ( y y1 ) = y y1 y y11 = y y( y1) = y 1 = y. Thus, for each y in the codomain, we can nd an x in the domain such that f ( x ) = y . Therefore, f is a surjection. 2...
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This note was uploaded on 02/25/2010 for the course MATHEMATIC 11007 taught by Professor Spyros during the Winter '10 term at Bristol Community College.
 Winter '10
 Spyros

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