Test 1 (COMP3560)-Introduction to Computer Theory Solve the following problems. Please write your answers in readable and clean form. 1. Consider a set of symbols -(a,b.c). (1) Find all strings in * shorter than 3. (2)Let 1-(A,ab, c}. Is L a language on ?Why? (3) Write L and ' 2. Fill the proper word in the blank (1) Given a grammar G, L(G) is the language by G (2) Given an automata M. L(M) is the language is the languagby M 3. Let 2- (a.b). Find the language generated by following grammar (1) A aA 1 (2) S bAal ba (3) S BA 4. (1) Find a grammar that generates language L = {ba": "12 0, n 2 1 }. 2) Find a grammar that generates language L (bm a2b 2 5. (1) Draw a transition graph for the dfa M-,5,q,,F),where -{%-44), {a, b), Fs(al and is defined as