1. Draw the derivation tree corresponding of w = aaabbaaa using the following context-free grammar %3D G = ({S), {a, b}, S, P) with productions S aSa, S bSb, S A. 2. Define properly nested parenthesis...

Extracted text: 1. Draw the derivation tree corresponding of w = aaabbaaa using the following context-free grammar %3D G = ({S), {a, b}, S, P) with productions S aSa, S bSb, S A. 2. Define properly nested parenthesis structures involving two kinds of parentheses, say () and ]. (Properly nested strings are (]), ([CO1), and [0], but not (D] or (0]. Define a context-free grammar for generating all properly nested parentheses. 3. Show that the grammar ({S}, {a, b}, S, P) with productions S - bSaS| aSbs |A is ambiguous. Draw two different parsing trees for a string that starts with b.