Please solve questions 1 and 3. for number one the figure is given

1. Which of the strings 0001, 01101,00001101 are accepted by the dfa in Figure 2.1? 2. Translate the graph in Figure 2.5 into -notation. 3. For ={a,b}, construct dfa's that accept the sets consisting of (a) all strings of even length. (b) all strings of length greater than 5 . (c) all strings with an even number of a 's. (d) all strings with an even number of a 's and an odd number of b 's. The graph in Figure 2.1 represents the dfa M=({q0,q1,q2},{0,1},,q0,{q1}), where is given by (q0,0)=q0,(q1,0)=q0,(q2,0)=q2,(q0,1)=q1,(q1,1)=q2,(q2,1)=q1. This dfa accepts the string 01. Starting in state q0, the symbol 0 is read first. Looking at the edges of the graph, we see that the automaton remains in state q0. Next, the 1 is read and the automaton goes into state q1. We are now at the end of the string and, at the same time, in a final state q1. Therefore, the string 01 is accepted. The dfa does not accept the string 00 , since after reading two consecutive 0 's, it will be in state q0. By similar reasoning, we see that the automaton will accept the strings 101, 0111, and 11001 , but not 100 or 1100