Question 3: (a) Complete the semantic rules below for Roman numerals, given that c-100, 1-50, x-10, v-5, i-1, and symbol values are added except: i before v or x indicates one less (e.g., iv is 4) and x before 1 or c indicates ten less (e.g., xc is 90). Use the rules to evaluate xcvii, showing all the steps. (3 marks) 1 KT-> C 2 KY> -> V 2 (b) The above grammar allows illegal forms such as xiiii or xxxxx. Add the 1 necessary attribute/s, semantic rule/s, and predicate/s to ensure that generated sentences contain groups of at most 3 i or 3 x. Draw a synthetized, decorated parse tree showing that 1viiii is not a valid Roman numeral. (4 marks)