# Suppose A is a countable subset of an uncountable set B. Show that B - A is uncountable. [duplicate]

Possible Duplicate:
Uncountable minus countable set is uncountable

Proposition:

Suppose A is a countable subset of an uncountable set B. Show that B - A is uncountable.

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## marked as duplicate by Brian M. Scott, Asaf Karagila, WimC, TMM, Henry T. HortonDec 14 '12 at 21:34

Suppose that $B-A$ is countable. Now we find that the union of $B-A$ and $A$ which is $B$ is countable (contradiction)