Let ℤ17 be the ring of integers modulo 17, and let ℤ×17 be the group of units of ℤ17 under multiplication. Which of the following are generators of ℤ×17? I.5 II.8 III.16 (I) 5.(II) 8.(III) 16.(A) None.(B) I only.(C) II only.(D) III only.(E) I, II, and III

Answer:  The correct option is (E) I, II and III.Step-by-step explanation:  Given that ℤ17 be the ring of integers modulo 17, and let ℤ×17 be the group of units of ℤ17 under multiplication. We are to select the correct generators of ℤ×17.According to the given information, we can writeℤ17 = {0, 1, 2, 3, . . . , 16}andℤ×17 = {1, 2 , 3 , . . . 16}.The generators of ℤ×17 are those elements which are co prime to 17.Since all the elements from 1 to 16 are co prime to 17, so all the elements of the set  ℤ×17 are its generators.Therefore, 5, 8 and 16, all are generators. So, i, ii and iii are generators.Thus, (E) is the correct option.