Texts: (Automata) Complete proof of how known closure properties and/or other information can be used to demonstrate closure of symmetric difference.
The symmetric difference of two sets is a new set that contains every element that is in either set except the elements that are in both sets. For example, the symmetric difference of {3, 7, 2, 12, 9} and {8, 12, 4, 16, 7, 5} would be {3, 2, 9, 8, 4, 16, 5}.
Prove that the family of regular languages is closed under symmetric difference.