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Here is a context-free grammar that can be used to generate algebraic expressions via the arithmetic operators (addition, subtraction, multiplication, and division), in the variables p, q, and r. The letter E stands for expression:
Rule 1: E -› pRule 2: E -› qRule 3: E -› rRule 4: E -› E + ERule 5: E -› E - ERule 6: E -› E X ERule 7: E -› E/ERule 8: E -›(E)
(i). Use the above grammar to derive the string given by the mathematical expression E = (p + q) X p - r X p/(q + q)
(ii). Provide a parse tree for this derivation.
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