Question 5[25 points] A linear grammar is one in which every rule has exactly one terminal and one non-terminal on the right hand side or just a single terminal on the right hand side or the empty string. Here is an example S aS|a|bB; B +bB\b. 1. Prove that any regular language can be generated by a linear gram- mar. I will be happy if you show me how to construct a grammar from a DFA; if your construction is clear enough you can skip the straight- forward proof that the language generated by the grammar and the language recognized by the DFA are the same. 2. Is every language generated by a linear grammar regular? If your answer is yes you must give a proof. If your answer is no you must give an example