I am working on the following exercise:
If $L_1,L_2$ are semidecidable, is $L_1-L_2 = \{w \mid w \in L_1 \text{ and } w \not\in L_2\}$ semidecidable?
I think that the claim is not true, but I can not find an easy counterexample. I think using something like $A_{TM}$ as $L_2$ might work, but I do not know what I should take as $L_1$. Could you please give me a hint?