In the exercises below, "e" will stand for the empty sequence of tokens. Also, since the main theme of these is arithmetic expressions, "E" will stand for a whole expression, instead of using "program". 1a. A grammar for simple nested parentheses is E-> (E) E - e Give a derivation and a parse tree for ((()). Write a grammar for arbitrary properly nested parentheses, such as (000). (Hint: Add E -> EE to #1) Draw a parse tree for (000). Give a leftmost derivation for (O)(). Give a rightmost derivation for ((0(). Write a grammar for arbitrary properly nested parentheses and brackets, such as ([](([]))). Draw a parse tree for ([](([0]))). Give a leftmost derivation for ((([O])))