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.

Please help.

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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Hint: Prove that the union of two countable sets is countable. – J. Loreaux Dec 14 '12 at 21:00

1 Answer

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

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