Construct a regular expression defining each of the following languages over the alphabet {a, b}.

(a) L = {aab, ba, bb, baab};

(b) The language of all strings containing exactly two b's.

(c) The language of all strings containing at least one a and at least one b.

(d) The language of all strings that do not end with ba.

(e) The language of all strings that do not containing the substring bb.

(f) The language of all strings in which every b is followed immediately by aa.