### Cardinality, Countability and Denumerable Sets

1. Show that if A and B are countable and disjoint, then A U B is countable. 2. Show that any set, A, of cardinality c contains a subset, B, that is denumerable. 3. Show that the irrational numbers have a cardinality c. 4. Show that if A is equivalent to B and C is equivalent to D, then A x C is equivalent to B x D.