$"($a$)$ Give a single regular expression that de$$nes a language for a new format of International Standard Book Numbers $($ISBNs$)$ such as $960-42-$AX$.[13]$ Strings in this language should have the following properties:

i$.$ They must be divided into exactly three sections, separated by hyphens. ii$.$ The $$rst section must be a non$-$empty sequence of digits. iii. The second section must be exactly two digits that de$$ne a number in the range zero to $$fty$.$ iv$.$ The third section must consist of an optional upper case letter, following by either an X or a Y$.$

$($b$)$ Consider the following context$-$free grammar where A is the start symbol.

A : B $|$ A $"",""$ A$.$ B : $""!""|""(""$ A $"")"".$

Draw two parse tre QL$03$ es that could result when parsing the valid input $(!),!,((!))$ using this grammar

$($c$)$ Rewrite the grammar from part $($c$)$ so that it is not ambiguous but still recognises the same strings. Which of the two trees you gave in part $($c$)$ is not a legal tree for the rewritten grammar?"