Final answer:
The union of sets A and C is {a, b, d, e, h, i, j, k}. The complement of the union is {c, f, g}.
Step-by-step explanation:
To find the union of sets A and C, we need to combine all the elements from both sets. Set A = {a, h, i, k} and set C = {b, d, e, j, k}.
The union of A and C, denoted by A ∪ C, includes all the elements that are in either A or C or in both.
Therefore, A ∪ C = {a, b, d, e, h, i, j, k}.
To find the complement of A ∪ C, denoted by (A ∪ C)', we need to find the elements that are not in A ∪ C but are in the universal set U = {a, b, c, d, e, f, g, h, i, j, k}.
Therefore, (A ∪ C)' = {c, f, g}.