I recently started self studying about algorithms and decision problem, so I don't have a firm grasp on this particular area. In this context I found myself thinking about the following .
If $L_1$ is semidecidable and $L_2$ is decidable, what can one say about the language set defined by their difference $L_3 = L_1 \text{ \ }L_2$ ?
I'm inclined to believ that $L_3$ is semidecidable, but I can't think of a way to prove it.
Any ideas?