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Unformatted text preview: B . (a) (1 point) Show that f ( i I A i ) = i I f ( A i ). (b) (1 point) Suppose f is a bijection. Show that f 1 ( i J B j ) = j J f 1 ( B j ). Problem 6: (1 points) or following functions, nd f ( A ) and f 1 ( B ). (a) (0.5 point) f : R R is dened by f ( x ) = sin x , A = { 2 , 1 , , 1 , 2 } , B = { , 1 , 2 } . (b) (0.5 point) f : R Z is is the oor function dened by f ( x ) = x = n where n x < n + 1 for n N and A = (0 , 5), B = { , 1 , 2 } . Problem 7: (2 points) Let f : A B and B B . (a) (1 point) Prove that f ( f 1 ( B ) ) B . (b) (1 point) Prove that if f is onto, then f ( f 1 ( B ) ) = B . Problem 8: (1 point) Prove or nd a counterexample to the following conjecture. Assume f : X Y and A, B X If f ( A ) \ f ( B ) = , then f ( A \ B ) = . 2...
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This note was uploaded on 10/18/2011 for the course MATH 19900 taught by Professor Schmidt during the Fall '07 term at UChicago.
 Fall '07
 SCHMIDT

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