Answers the following:

a- Construct a syntax-directed translation scheme that translates arithmetic expressions from infix notation into prefix notation in which an operator appears before its operands; e.g., xy is the prefix notation for x y. Give annotated parse trees for the inputs 9-5+2 and 9-5*2.

b- Construct a syntax-directed translation scheme that translates integers into roman numerals.

c- Construct a syntax-directed translation scheme that translates postfix arithmetic expressions into equivalent infix arithmetic expressions