Assignment:
1. Show that if A and B are countable and disjoint, then A 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.
Provide complete and step by step solution for the question and show calculations and use formulas.