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Problem 4. Consider ? : (Z100, +100) ? (Z100, +100) defined by ?([x]100) = [41x +...

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Problem 4. Consider ? : (Z100, +100) ? (Z100, +100) defined by?([x]100) = [41x + 19]100. a.) Show that ? is well-defined. b.) Usethe fact that 61 · 41 = 2501 to argue that the function ? isone-to-one. c.) Is ? onto? Why or why not. Suppose that y is in theimage of ?, find an element x so that ?(x) = y. [The answer will bedependent on the value of y.] Then prove that the found elementworks. d.) Is ? a homomorphism?

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