Use the set of productions to show that each of these sentences is a valid sentence. a)

Question:

Use the set of productions to show that each of these sentences is a valid sentence.
a) The happy hare runs
b) The sleepy tortoise runs quickly
c) The tortoise passes the hare
d) The sleepy hare passes the happy tortoise
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:

Adjective †’ sleepy
Adjective †’ happy
Noun †’ tortoise
Noun †’ hare
Transitive verb †’ passes
Intransitive verb †’ runs
Adverb †’ quickly
Adverb †’ slowly