
Concept explainers
Exercises 1-3 refer to the grammar with start symbol sentence, set of terminals T = {the, sleepy, happy, tortoise, hare, passes, runs, quickly, slowly}, set of non-terminals 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
1. 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

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Chapter 13 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
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