The elements of order 8 in the group (Zg ,+) is a)4 b) 5 c)6 d) 8

a) Find a generating set of U(20) with two elements. b) Use the generators you found in part (a) and the diagram below to draw a Cayley digraph of U(20).

1. Determine whether (Q.), where a bab/2 for all a, b € Q is a group or not. a) show step for associative. b) show step for identity. c) show step inverse. 2. A permutation is an arrangement of objects in a definite order. The a and I are given as follows: a) Find ar. b) Find TT-¹. 3. A ring are defined busing THREE (3) axioms that need to satisfy such as Abelian Group, Associative and Distributive Laws. Hence, show that is a ring. 4. Explain the difference between Isomorphism and Homomorphism.

251 Is the grouporder 539 simple? Explain