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## Homework Statement

If the cardinality of A is less than or equal to the cardinality of the reals and the cardinality of B is less than or equal to the cardinality of the reals, I need to show that the cardinality of the union of A and B is less than or equal to the cardinality of the reals.

IE: Prove that if |A|</=|R| and |B|</=|R|, then |AUB|</=|R|.

Thanks for any help. I am in a basic analysis class, and we just started a small section on cardinality.

## Homework Equations

## The Attempt at a Solution

All I know is that based on my assumption, I know that there is a 1-1 function from A to the real numbers and another 1-1 function from B to the real numbers.