Theory of Computation: Regular Expression & Context-Free Grammar

Please kindly show each step of your working towards the final result with explanation wherever applicable. Thank you.

1. Let ?-a, b, c}. Write a regular expression for the set of all strings in ?* such that the sum of the number of a's and b's in the string is at most two. For example, the strings ab and ba are in the language, but aaabb is not in the language. 2. Give context-free grammars that generate the following languages (a) The language w E 10, 1)* | the length of w is odd and the middle symbol is 0 (b) The language {a b ck i,j, k 2 0, and i jori k) (c) The language \a" bm |m ^n ^ 2m). (d)