Is this set recursively enumerable/recursive? I've recently started studying the ideas behind algorithms. That being said, I found myself browsing through different sorts of problems in order to get a better grasp on the subject.
Inspired by this question, I'm going to ask for a few more details, as I find myself unable to understand the answer. Precisely, what I would like to know is :
Given two sets, $L_1$ and $L_2$, such that $L_1$ is recursive and $L_2$ is recursively enumerable but not recursive, what can one say about $L_3 = L_1 -L_2$ and what's the formal reasoning behind it?

Note that $L_3^C$ is recursively enumerable as $L_3^C=L_2\cup L_1^C$ and both $L_2$ and $L_1^C$ are recursively enumerable.
Hence, as Crostul explained in comments, either $L_3$ is recursively enumerable (for example if $L_1$ is finite and so $L_3$ is recursive) or is not (for example if $L_1=\mathbb N$ and so $L_3$ is co-r.e.).
