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Unformatted text preview: MATH S104 Lecture 4 Inclass Problem Solutions July 2, 2009 Problem 1 : Let X = { 1 , 3 , 5 } and Y = { a,b,c,d } . Draw an arrow diagram that defines a function f with each of the following characteristics, or explain why such a function cannot exist. a) f is not a welldefined function. a b c 1 3 5 d a b c 1 3 5 d The arrow diagram on the left is not welldefined because 3 has no image in Y . The diagram on the right is not a welldefined function because 1 is mapped to multiple images in Y . b) f is not a welldefined function, but f 1 is. a b c 1 3 5 d a b c 1 3 5 d c) f is a function that is onetoone but not onto. a b c 1 3 5 d f is not onto because b has no preimage in X . d) f is a function and f 1 is a function. Such a function is not possible with the specified domain and codomain, because Y ≠ X . 1 Problem 2 * : Find at least three different sequences beginning with the terms 1,2,4 whose terms are generated by a simple formula....
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 Spring '10
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 Mathematical Induction, Recursion, Inductive Reasoning, Mathematical logic, inductive step

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