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Unformatted text preview: X with 5 elements to a set Y with 7 elements? How many of these functions are injective? 4. (a) For every integer n 1 let f ( n ) be dened by the formula f ( n ) = P n k =1 (3 k 2). Compute f (1), f (2), and f (3). (b) Fill in the blank to make a true statement: f ( n + 1) = f ( n ) + : (c) Use induction to prove that for every integer n 1, n X k =1 (3 k 2) = n (3 n 1) 2 : 5. Let A be a 10 element subset of f 1 ; 2 ; 3 ; :::; 50 g . Show that A possesses two dierent 4element subsets, the sums of whose elements are equal. Hint: Use the pigeon hole principle. Math 4023 1...
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This document was uploaded on 12/28/2011.
 Fall '09

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