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Which among the following is incorrect with reference to a derivation tree?
- a)Every vertex has a label which is a terminal or a variable.
- b)The root has a label which can be a terminal.
- c)The label of the internal vertex is a variable.
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
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Which among the following is incorrect with reference to a derivation ...
The root or interms of the grammar, starting variable can not be a terminal.
Most Upvoted Answer
Which among the following is incorrect with reference to a derivation ...
Understanding Derivation Trees
A derivation tree is a graphical representation used in formal language theory to illustrate the structure of strings generated by a grammar. Each node in the tree represents a variable or terminal, showcasing the production rules applied.
Key Characteristics of Derivation Trees
- Every Vertex Label: Each vertex in a derivation tree must be labeled with either a terminal symbol (a symbol from the language) or a variable (a symbol used in the grammar). This is crucial because it indicates the elements involved in the derivation process.
- Root Label: The root of the tree represents the starting symbol of the grammar. It is essential that the root label is a variable, not a terminal. Thus, the statement that "the root has a label which can be a terminal" is incorrect.
- Internal Vertex Labels: Internal vertices in the tree represent variables from the grammar. This structure allows the tree to expand into terminal symbols as the derivation progresses.
Conclusion
The correct interpretation of derivation trees is pivotal in understanding how grammars and languages work. The incorrect assertion in option 'B' highlights a fundamental aspect of derivation trees: the root must always be a variable, not a terminal. Therefore, the statement in option 'B' is indeed the incorrect one.
A derivation tree is a graphical representation used in formal language theory to illustrate the structure of strings generated by a grammar. Each node in the tree represents a variable or terminal, showcasing the production rules applied.
Key Characteristics of Derivation Trees
- Every Vertex Label: Each vertex in a derivation tree must be labeled with either a terminal symbol (a symbol from the language) or a variable (a symbol used in the grammar). This is crucial because it indicates the elements involved in the derivation process.
- Root Label: The root of the tree represents the starting symbol of the grammar. It is essential that the root label is a variable, not a terminal. Thus, the statement that "the root has a label which can be a terminal" is incorrect.
- Internal Vertex Labels: Internal vertices in the tree represent variables from the grammar. This structure allows the tree to expand into terminal symbols as the derivation progresses.
Conclusion
The correct interpretation of derivation trees is pivotal in understanding how grammars and languages work. The incorrect assertion in option 'B' highlights a fundamental aspect of derivation trees: the root must always be a variable, not a terminal. Therefore, the statement in option 'B' is indeed the incorrect one.
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Which among the following is incorrect with reference to a derivation tree?a)Every vertex has a label which is a terminal or a variable.b)The root has a label which can be a terminal.c)The label of the internal vertex is a variable.d)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?
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