Why if $A$ is a set of second category and $B$ is a set of first category, then $A \setminus B$ is of second category? (I am a native Spanish speaker, so that forgive me if my English is not perfect)
I know that a set is of second category if it is not of first category, and that a set is of first category if it is the union of countably many nowhere dense sets. Many thanks to all those who will try to help me.
Exercise: show that if $E$ and $F$ are two sets of first category, then $E \cup F$ is also of first category.
Now if $A \setminus B$ were of first category, then writing $A = B \cup (A \setminus B)$ would imply...?