Question

Show that the hare runs the sleepy tortoise is not a valid sentence.

Short answer

Hence, it is proved that the hare runs the sleepy tortoise is not a valid sentence.

Step-by-step solution

Describe the sentences of a formal language using grammar.

The use of grammar helps when we consider the two classes of problems that arise most frequently in applications to programming languages:

(1) How can we determine whether a combination of words is a valid sentence in a formal language?

(2) How can we generate valid sentences in a formal language? Before giving a technical definition of grammar.

Firstly, Use the set of productions.

Suppose \({\bf{G = }}\left( {{\bf{V, T, S, P}}} \right)\) is a phrase structure grammar with the starting symbol.

\({\bf{S = sentence, the set of terminuses}}\)

\({\bf{T = }}\left\{ \begin{array}{l}{\bf{Them sleepy, happy, tortoise, bare,}}\\{\bf{ passes, runs, quickly, slowly}}\end{array} \right\}{\bf{The set of non - terminals}}\)

\({\bf{N = }}\left\{ \begin{array}{l}{\bf{noun phrase, transitive verb phrase, intransitive verb phrase,}}\\{\bf{ article, adjective, noun, verb, adverb}}\end{array} \right\}{\bf{ and productions}}{\bf{.}}\)

\({\bf{Sentence}} \to {\bf{noun phrase transitive verb phrase noun phrase}}\)

\({\bf{Sentence}} \to {\bf{noun phrase intransitive verb phrase}}\)

\({\bf{Noun phrase}} \to {\bf{article adjective noun}}\)

\({\bf{Noun phrase}} \to {\bf{article noun}}\)

\({\bf{Transitive verb phrase}} \to {\bf{transitive verb\;}}\)

\({\bf{Intransitive verb phrase}} \to {\bf{intransitive verb adverb}}\)

\({\bf{Intransitive verb phrase}} \to {\bf{in transitive verb}}\)

\({\bf{Article}} \to {\bf{the}}\)

\({\bf{Adjective}} \to {\bf{sleepy}}\)

\({\bf{Adjective}} \to {\bf{happy}}\)

\({\bf{Noun}} \to {\bf{tortoise}}\)

\({\bf{Noun}} \to {\bf{hare}}\)

\({\bf{Transitive verb}} \to {\bf{passes}}\)

\({\bf{Intransitive verb}} \to {\bf{runs}}\)

\({\bf{Adverb}} \to {\bf{quickly}}\)

\({\bf{Adverb}} \to {\bf{slowly}}\)

We shall show that the hare runs the sleepy tortoise is not a valid

The only way to get a noun, such as a tortoise, at the end is to have a noun phrase at the end, which can be achieved only via the production sentence.

(1) Noun phrase transitive verb phrase noun phrase. However, transitive verb phrase transitive verb Passes and this sentence do not contain passes.

(2) Therefore, “The hare runs the sleepy tortoise” is not a valid sentence because it is in the form Sentence.

(3) Noun phrase intransitive verb phrase noun phrase, which is not a production

Hence, the hare runs the sleepy tortoise is not a valid sentence.