Decidability language, intersection I have two langages $ A, B \in \mathrm{coRE}$.  How can I prove that $ A \triangle B= ( A - B) \cup (B - A)$ is also in $\mathrm{coRE}\,$?
The language $A = \Sigma^*$ is coRE. Since $A \triangle B = \overline{B}$, the statement you are trying to prove implies RE=coRE, which is known to be false: for example, the set of all programs that halt is in RE but not in coRE.