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.
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Cardinality, countability and denumerable sets are investigated. The solution is detailed and well presented.