For each of the following statements, indicate whether it is true or false, and justify your answer .

(a) Every subset of a regular language is regular.

(b) Every regular language has a regular proper subset.

(c) Let A = B C. If A is regular and C is regular, B must be regular.

(d) If L is regular, then so is {xy : x L and y 6 L}.

(e) L = {w : w = w R} is regular.

(f) If L is regular, then so is {w : w L and w R L}.

For each of the following statements, indicate whether it is true or false, and justify your answer [12 pointsl. (a) Every subset of a regular language is regular (b) Every regular language has a regular proper subset (c) Let A-BnC. If A is regular and C is regular, B must be regular (d) If L is regular, then so is {ry: xEL and y # L) (e) L-(w : w = wR} is regular. (f) If L is regular, then so is w E L and wREL