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# Give an example of two uncountable sets A and B such that A − B is a) finite. b) countably infinite. c) uncountable.

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DEFINITIONS

A set is $\textbf{finite}$ if it contains a limited number of elements (thus it is possible to list every single element in the set).

A set is $\textbf{countably infinite}$ if the set contains an unlimited number of elements and if there is a one-to-one correspondence with the positive integers.

A set is $\textbf{uncountable}$ if the set is not finite or countably infinite.

$\textbf{Difference}$ $A-B$: All elements in $A$ that are NOT in $B$ (complement of $B$ with respect to $A$).

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