6. 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 I'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 O's and l'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)* 3. (012)* 4. (01+2)* O a) Perm(L((01)*)) is context-free but not regular. O b) Perm(L((012)*)) is context-free but not regular. c) Perm(L((01+2)*)) is not context-free d) Perm(L(0*+1*) is context-free but not regular. 6. 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 I'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 O's and l'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)* 3. (012)* 4. (01+2)* O a) Perm(L((01)*)) is context-free but not regular. O b) Perm(L((012)*)) is context-free but not regular. c) Perm(L((01+2)*)) is not context-free d) Perm(L(0*+1*) is context-free but not regular