Q1 Construct a DFA recognizing the following language over the alphabet {a,b}*:

A) The set of all strings that begin with a but do not contain aab as a substring.

B) L={x | the substring abb occurs exactly two times}

C) L={xcycz | x,y {a,b}* , #_ax + #_by +#_az is divisible by 3} (where #a, #b, #a denotes the number of a,b in x,y and z respectively)

Q2 What can be said about the language L= { w {a,b}* | abw = wba }? Is it the empty string? Is it Regular?