I'm sorry to bother since I suppose my problem is pretty easy to find an answer to, I just can't find anything in gogle, or better, I'm not really sure how to google my problem.
I'm studying for my Discrete Math Exam, and an old question (don't have the solutions) goes as follows:
The Set $A\setminus B$ is countable. Set $A$ is uncountable. What conclusion can you draw about the un/countability of $B$?
I've been trying to apply the properties of in/sur/bijections but it's too general to be applied here. It must be some set operation rule I'm missing that I can't find.
Appreciate your help.
Note that $A=(A\setminus B)\cup(A\cap B)$. So, since $A$ is uncountable and $A\setminus B$ is countable, $A\cap B$ has to be uncountable, and therefore $B$ has to be uncountable.