Question: A regular expression for the language over the alphabet {a, b} with each string having an even number of b's is (a*ba*ba*)*a*. Use this

 A regular expression for the language over the alphabet {a, b} with  

A regular expression for the language over the alphabet {a, b} with each string having an even number of b's is (a*ba*ba*)*a*. Use this result to find regular expressions for the following languages a. a language over the same alphabet but with each string having odd number of b's. b. a language over the same alphabet but with each string having 4n+1 (n >= 0) b's. If a regular expression for the language over the alphabet {a, b} with no string containing the substring aa is (b+ab)*(A+a), then what is the regular expression for the language over the alphabet {a, b, c) with no string containing the substring aa?

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