(Thanks to David Liben-Nowell) The symmetric difference A Δ B of two sets A ⊆ Σ* and B ⊆ Σ* consists of strings that are elements of either A or B, but not both. Formally, A Δ B = {x ∈ Σ* | x ∈ A iff x ∉ B} Your job for this exercise is to prove that if A and B are regular, then A Δ B is also regular.