1,87 t a) If A and B are each countable sets, show that AUB is countable. (Hint: For each set, consider a sequence of all elements, and show how to splice the sequences together to make one sequence....

Extracted text: 1,87 t a) If A and B are each countable sets, show that AUB is countable. (Hint: For each set, consider a sequence of all elements, and show how to splice the sequences together to make one sequence. Remember that the sets need not be disjoint.) b) Prove that the union of countably many finite sets is either countable or finite.