For strings w and t, write w ≗ t if the symbols of w are a permutation of the symbols of t. In other words, w $ t if t and w have the same symbols in the same quantities, but possibly in a different order.

For any string w, define SCRAMBLE(w) = {t| t ≗ w}. For any language A, let SCRAMBLE(A) = {t| t ∈ SCRAMBLE(w) for some w ∈ A}.

a. Show that if Σ = {0,1}, then the SCRAMBLE of a regular language is context free.

b. What happens in part (a) if Σ contains three or more symbols? Prove your answer.