The Parse Tree for a Given String in Context-Free Grammar

To understand the given statement, let's break it down and explain each component.

Context-Free Grammar (CFG)
A context-free grammar is a formal grammar consisting of a set of production rules that define the syntax of a language. It consists of a set of non-terminal symbols, a set of terminal symbols, a start symbol, and a set of production rules that define how the non-terminal symbols can be rewritten as strings of terminal and non-terminal symbols.

Belongs to L(G)
The notation "w belongs to L(G)" means that the string 'w' is a valid string in the language defined by the context-free grammar G. In other words, 'w' can be derived from the start symbol of G using the production rules of G.

Parse Tree
A parse tree is a graphical representation of the syntactic structure of a string according to the rules of a context-free grammar. It shows how the string can be derived from the start symbol of the grammar by applying the production rules. The nodes of the parse tree represent the non-terminal symbols, and the edges represent the production rules.

Syntactic Structure
The syntactic structure of a string defines the hierarchical relationship between the components of the string. In the case of a programming language, SQL query, or XML document, the syntactic structure defines the structure of statements, queries, or tags in the respective language.

Explanation of the Correct Answer (Option D)
The correct answer is option D, which states that if 'w' belongs to L(G), then 'w' could be a program, an SQL query, or an XML document. This is because all of these can be described by context-free grammars.

- Program: A program in a programming language can be described by a context-free grammar. The grammar defines the syntax of the language, including statements, expressions, and control structures. The parse tree for a program shows the hierarchical structure of the code.

- SQL Query: An SQL query is a statement written in the SQL language used to retrieve data from a database. SQL has a well-defined syntax that can be described by a context-free grammar. The parse tree for an SQL query represents the structure of the query, including the select statement, conditions, and joins.

- XML Document: An XML document is a structured document that follows the rules of the XML language. XML has a context-free grammar that defines its syntax, including tags, attributes, and nested elements. The parse tree for an XML document represents the hierarchical structure of the document.

In conclusion, the statement is correct because if a string belongs to the language defined by a context-free grammar, it can have a parse tree that defines its syntactic structure. This applies to programs, SQL queries, and XML documents, as they can all be described using context-free grammars.