# Prove that if A is an uncountable set and B is a countable set, then A-B must be uncountable

I am having difficulty proving that A-B must be uncountable using proof by contradiction considering (A-B) ∪ B )

Any help?

If $A-B$ is countable, then $(A-B)\cup B$ is also countable. But $A=(A-B)\cup B$ is uncountable.

• In general, $A\neq(A-B)\cup B$. But $A\subset(A-B)\cup B$, which is enough. Sep 18, 2016 at 17:44