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3. (40) Context Free Grammar. (a) Write a context free grammar for arithmetic expressions which can use numbers, variables and operation + only. (b) Write a context free grammar for the arithmetic expressions above that captures right associativity. (c) Write a context free grammar for arithmetics expressions which can use numbers, variables and binary operations - and + only. Your grammar has to capture the precedence that - must be computed before +. For example 5 + 5 - 5 - 5 + 6 - 5 should be computed as 5 + (5 -5 -5) + 6-5). (d) Refine your grammar above to allow parenthesis (and ). Hint. Recall the techniques on how precedence and associativity were dealt with in the class