Question 3 In each of the following cases, check whether the given subset is (1) an ideal, (2) a maximal ideal, (3) a principal ideal, and (4) a prime ideal. Justify your answer. (a) I= {0,2} in Z4. (b) U = {q(x) = Z3 [x]: x²+x+1 is a factor of q(x)} in Z3 [x]. (c) J = {a+i b: 17a - 190a²b² > 0} in Q(i) = {a+i.b: a,b € Q}, where i EC is the imaginary unit (i² = -1).

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