The grammar with start symbol sentence, set of terminals T = {the, sleepy, happy, tortoise, hare, passes, runs, quickly, slowly}, set of nonterminals N = {noun phrase, transitive verb phrase, intransitive verb phrase, article, adjective, noun, verb, adverb}, and productions: sentence → noun phrase transitive verb phrase noun phrase sentence → noun phrase intransitive verb
phrase noun phrase → article adjective noun
noun phrase → article noun transitive verb
phrase → transitive verb intransitive verb
phrase→intransitive verb adverb
intransitive verb
phrase → intransitive
verb article → the
Adjective → sleepy
adjective → happy
noun → tortoise noun → hare
transitive verb → passes
intransitive verb → runs
adverb → quickly
adverb → slowly
The correct answer and explanation is :
Correct Answer:
This grammar defines a simple language structure. Here are a few valid sentences generated using the given grammar:
- The sleepy tortoise passes the happy hare.
- The hare runs quickly.
- The happy tortoise passes the sleepy hare.
- The tortoise runs slowly.
Explanation:
This is a context-free grammar (CFG) with the start symbol sentence. Let’s break down its components:
- Terminals (T): These are the words that appear in the final sentence.
- Articles: the
- Adjectives: sleepy, happy
- Nouns: tortoise, hare
- Verbs: passes, runs
- Adverbs: quickly, slowly
- Non-terminals (N): These represent categories of words or phrases, which can be replaced using production rules.
- sentence: The starting point, which expands into noun and verb phrases.
- noun phrase: A phrase containing an article, an optional adjective, and a noun.
- transitive verb phrase: Contains a transitive verb and connects to another noun phrase.
- intransitive verb phrase: Contains an intransitive verb and an optional adverb.
- Production Rules:
- A sentence can be structured as noun phrase + transitive verb phrase + noun phrase (e.g., The tortoise passes the hare).
- A sentence can also be noun phrase + intransitive verb phrase (e.g., The hare runs quickly).
- A noun phrase can be constructed using an article, an adjective, and a noun (The happy tortoise).
- A verb phrase can include a transitive verb (passes) or an intransitive verb plus an adverb (runs slowly).
By following these rules, we can generate syntactically correct sentences within this small language.
