For each i=1,2, and 3, compose a grammar G_i^, such that L(G_i) = H_i, where

(30 point)Foreach and 3, compose a grammar G, such that L(G) Hi, where (a) H L(M1) where M is the following DFA: 1 42 93 0,1 FIGURE 1.4 A finite automaton called M1 that has three states Figure 1: DFA Mi (from Sipser, Chapter 1) State, for each grammar G (i = 1, 2, 3), the set of variables, the set of terminals, the set of production rules, with each rule being a variable and a string of variables and terminals, and, the start variable. for the grammar clearly. Give reason(s) to support your answer to each case. The reason(s) given for each case should be concise. Do not use more than three complete sentences for each case