4ii. The order of an element is the number of copies of that element that must be `added' together to obtain the identity element of the group.
The identity element in the first group is e, so we have:
o(e) = 1,
o(a) = 2 since a * a = e,
o(b) = 2 since b * b = e,
o(c) = 2 since c * c = e.
The identity element in the second group is 0, so we have:
o(0) = 1,
o(1) = 4 since 1 + 1 = 2, 1 + 1 + 1 = 3, and 1 + 1 + 1 + 1 = 0,
o(2) = 2 since 2 + 2 = 0,
o(3) = 4 since 3 + 3 = 2, 3 + 3 + 3 = 1, and 3 + 3 + 3 + 3 = 0.