Please do not copy-paste answer from other questions. Detailed and clear answer is most appreciated.

Please do not copy-paste answer. Detailed and clear answer is most appreciated.

a) Prove that the language L = {(D)D is a DFA that accepts an even length string} is decidable. b) What is wrong with the following proof? Why? T="On input string (D): 1. Check whether D represents a valid DFA. 2. Run D on the even length strings one by one. If it accepts one of them accept. Oth- erwise, reject." T is a decider, therefore, L is decidable