(a) Give an example of two countably infinite sets A1 ⊆ N and A2 ⊆ N such that A1 ∪ A2 = N and A1 ∩ A2 = ∅.
(b) Use part (a) to prove a general result: If S1 and S2 are countably infinite sets and S1 ∩ S2 = ∅, then S1 ∪ S2 is countably infinite.
(c) Using the result in part (b) and results known from class regarding the cardinality of R, prove that the set of irrational numbers R - Q is not countably infinite.