5. Figure (a) gives the addition table for Z4, the integers modulo 4 under addition; and Figure (b) gives the partial multiplication table for S = {1, 3, 7, 9) in Z10. Are (Z4, +) and (S, x) semi-groups, monoids or groups? Find out a homomorphism mapping between (Z4, +) and (S, x). + 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 3 0 1 2 (a) X 1 3 7 9 1 1 3 7 3 9 1 9 3 3 7 1 9 7 (b) 9 7 9 7 3 1

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Q: 4 Let f = (4 5 6) and g = (1984) (275) (36) be two permutations in S9. (a) Compute fogo f-1, and…

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