(5 points) Which of the following are valid regular expressions over the alphabet a, b? Valid regular expressions are those that are built up using Definition 1.52 on page 64 of the book, allowing also the conventions on pages 63-65. Answer VALID for those that are, and ERROR for those that aren't (a) aa (b) aU (bu) (c) a"bm (d) {(aUb)*) (e) a(ab)b DEFINITION 1.52 Say that R is a regular expression if R is a in the alphabet , I. a for some 2. e, 3. 0, 4. (R1 U R2), where Ri and R2 are regular expressions, 5. (RI o R2), where Ri and R2 are regular expressions, or 6. (RI), where Ri is a regular expression In items 1 and 2, the regular expressions a and represent the languages (a) and (e], respectively. In item 3, the regular expres- sion represents the empty language. In items 4, 5, and 6, the expressions represent the languages obtained by taking the union or concatenation of the languages Ri and R2, or the star of the language Ri, respectively