The operation Perm(w), applied to a string w, is all strings that can be constructed by permuting the symbols of w in any order. For example, if w = 101, then Perm(w) is all strings with two 1's and one 0, i.e., Perm(w) = {101, 110, 011}. If L is a regular language, then Perm(L) is the union of Perm(w) taken over all w in L.

For example, if L is the language L(0*1*), then Perm(L) is all strings of 0's and 1's, i.e., L((0+1)*). If L is regular, Perm(L) is sometimes regular, sometimes context-free but not regular, and sometimes not even context-free. Consider each of the following regular expressions R below, and decide whether Perm(L(R)) is regular, context-free, or neither:

1. (01)*

2. 0*+1*

3. (012)*

4. (01+2)*

a) Perm(L((012)*)) is not context-free.

b) Perm(L((01)*)) is not context-free.

c) Perm(L((012)*)) is context-free but not regular

d) Perm(L(0*+1*)) is context-free but not regular.

Someone can explain me