# Cardinality, Countability and Denumerable Sets

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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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#### Solution Summary

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

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