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Unformatted text preview: then all three are empty. (12) 5. a. Let f:NxN>N be given by f(m,n) = 2^m(2n+1). Find f1(B) where B = {4,6,8,10,12,14}. b. Suppose f:A>B. Then, if we consider the induced set function f from P(A) to P(B) and the induced set function f1 from P(B) to P(A), where P denotes the power set, indicate if it is true or false that f1(f(X)) = X, for all subsets X of A. If so, why? If not, why not? (9) 6. a. Prove that any set equivalent to a finite set must be finite. b. Prove directly (do not cite any theorems) that the interval (infinity, a) is equivalent to the interval (b, infinity). (20) 7. Prove that if A is a denumerable set, then AxAxAx . . . xA (A appears n times) is denumerable, for any natural number n. (14)...
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 Winter '10
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