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Unformatted text preview: x * x = e . (Hint: calculate x * ( x * x )). 2. (a) Show that multiplication is a well-deFned binary operation on the set Z n of con-gruence classes of integers modulo n . (b) Given an integer n > 1, let Z n be the set of elements x Z n such that there exists y Z n with xy = 1. Show that Z n with the operation of multiplication is a group. (c) Write multiplication tables for Z 8 , Z 10 , and Z 12 . (d) Show that Z 8 and Z 12 are isomorphic, but that Z 10 is not isomorphic to Z 8 and Z 12 . 3. raleigh, section 4, exercises 9, 32, 41. 4. raleigh, section 5, exercises 13, 51, 54. 5. How challenging did you Fnd this assignment? How long did it take?...
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- Spring '08