4. Suppose that the sets A, B, and their complements A', B', are recursively enumerable (r.e.). Is the set C = A' union B recursive ? Present a formal proof. 5. Suppose that the set D is only r.e. Is the set E =D union D' recursive ? 6. Show that for any positive integer k, the line segment (1/2k, 1/k) contains uncountably many irrational numbers. 4. Suppose that the sets A, B, and their complements A', B', are recursively enumerable (r.e.). Is the set C = A' union B recursive ? Present a formal proof. 5. Suppose that the set D is only r.e. Is the set E =D union D' recursive ? 6. Show that for any positive integer k, the line segment (1/2k, 1/k) contains uncountably many irrational numbers