For an assignment I have to proof that for two given decidable languages A,B, A\B is decidable too.
My idea is as follows: If B is empty or doesnt have elements in common with A, then A\B is decidable because A\B=A.
If B is not empty and intersects with A, A\B is just a smaller subset of A and therefore decidable.
I have a feeling that this is either the wrong idea or not formalized enough. I would really appreciate any hints regarding that.
EDIT: A subset of a decidable language is NOT always decidable too, this was a misconception.
Thanks in advance