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 —› p
Rule 2: E —› q
Rule 3: E —› r
Rule 4: E —› E + E
Rule 5: E —› E – E
Rule 6: E —› E X E
Rule 7: E —› E/E
Rule 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.
