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Unformatted text preview: MATH 239 Assignment 1 Spring 2007 This assignment is due at noon on Friday, May 11, 2007, in the drop boxes opposite the Tutorial Centre, MC 4067. 1. A onetoone correspondence is a function f : A B which is both onetoone and onto. If a function f : A B has the property that x 6 = y f ( x ) 6 = f ( y ), then we say that f is onetoone . Function f is said to be onto if, for every z B , there is an x A such that f ( x ) = z . (Onetoone correspondences are an important enumerative technique, but we only touch on them briefly in Section 1.1 of MATH 239.) Determine whether or not each function defined below as onetoone, or onto, or both. Briefly justify your answer. (a) Let f : Z Z be defined as f ( n ) = 2 n 2 + 5. (b) Let g : Z Z be defined as g ( n ) = 5 2 n . (c) Let B = { b 1 b 2 . . . b 10 : b i { , 1 } i, 1 i 10 } be the set of all binary strings of length 10, and let S be all subsets of { 1 , 2 , . . . 10 } ....
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This note was uploaded on 01/17/2011 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.
 Spring '09
 M.PEI
 Math

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