Let U(n) be the set of all positive integers less than n and relatively prime to...

  

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Let U(n) be the set of all positive integers less than n and relatively prime to n. The set U(10) {1,3,7,9} is a group under the multiplication modulo 10 operation. (a) (b) (c) (d) Construct a Cayley table for U(10). Using the Cayley table constructed in (a), identify a proper nontrivial subgroup in U(10). Explain your answer. Compute the order of each element in U(10). Hence, determine whether U(10) is cyclic. Show that Z4 under addition operation is isomorphic to U(10). Let U(n) be the set of all positive integers less than n and relatively prime to n. The set U(10) {1,3,7,9} is a group under the multiplication modulo 10 operation. (a) (b) (c) (d) Construct a Cayley table for U(10). Using the Cayley table constructed in (a), identify a proper nontrivial subgroup in U(10). Explain your answer. Compute the order of each element in U(10). Hence, determine whether U(10) is cyclic. Show that Z4 under addition operation is isomorphic to U(10).