How can we prove that an enumerable/decidable group of languages is closed under an operation? For example:

If the XOR operation on two languages, A and B, is described as:
$A\;\mathrm{XOR}\;B = (A \cup B) \setminus (A \cap B)$,

1) How can we prove that the set of enumerable languages is closed under the XOR operation?

2) How can we prove that the set of decidable languages is closed under the XOR operation?
Here is a similar example, with the minority operator: the minority of three languages $A,B,C$ consists of words belonging to at most 1 of $A,B,C$.

If $A,B,C$ are decidable then so is their minority. Indeed, given a word $w$, first determine whether $w$ belongs to $A$, to $B$, and to $C$. You can do this since $A,B,C$ are decidable. Depending on this data, either accept or reject $w$. This is an algorithm deciding the minority.

If $A,B,C$ are enumerable, then their minority need not be so. Indeed, let $A$ be a language which is enumerable but not co-enumerable (for example, the set of halting programs). The minority of $A,A,A$ consists of all words not in $A$, i.e., the complement of $A$. By assumption $A$ is not co-enumerable, so the minority of $A,A,A$ is not enumerable.