Final answer:
A set of terminal symbols in a CFG is the collection of basic symbols that compose the language. These symbols, which include characters like digits and operators in the case of arithmetic expressions, are the endpoints of production rules and are not expandable. Terminal symbols are distinct from nonterminal symbols, which can be further replaced or expanded in the grammar.
Step-by-step explanation:
Understanding Terminal Symbols in CFG
In the context of a Context-Free Grammar (CFG), a set of terminal symbols refers to the basic symbols from which strings (sentences) of the language can be constructed. By definition, a CFG is composed of a set of rules that are used to convey meaning through the combination of symbols from a given lexicon. The role of terminal symbols is analogous to the leaves of a syntax tree - they cannot be replaced further by production rules. Unlike nonterminals, which can be expanded into sequences of terminals and/or nonterminals, terminal symbols are the actual characters or tokens that appear in the language strings.
For example, in the CFG defining simple arithmetic expressions, the terminal symbols might include the digits 0-9 and the operators +, -, *, and /. These are the characters that would appear in a well-formed arithmetic expression.
A key concept to understand when working with grammars and languages is the distinction between terminal and nonterminal symbols. Terminal symbols, being the end point of production applications, do not have rules that describe how they can be replaced or subdivided; they are the atomic elements of the grammar.
Another important point is that while terminal symbols are the vocabulary of the language defined by a CFG, the grammar’s production rules and the structure they impose provide the syntax. This is an essential aspect of a grammar set of rules that needs to be well understood in Computer Science and Linguistics.