Let E be an alphabet and A C E*. (a) If c E E and A C E*, we define APPEND(A) as {wc E E* | w E A}. Prove that, if A is a regular language, then APPEND(A) is a regular language. (b) Let DA be a DFA...

Extracted text: Let E be an alphabet and A C E*. (a) If c E E and A C E*, we define APPEND(A) as {wc E E* | w E A}. Prove that, if A is a regular language, then APPEND(A) is a regular language. (b) Let DA be a DFA recognizing A. Describe an NFA NA recognizing APPENDe(A) using only one more state than DA. Give a brief argument that your NFA recognizes A.