Question

4. What is the language described by the grammar? How many sentences does the language contain?

<Z> ::= <L> | <L> <L> | <L> <L> <L>

<L> ::= a | b | c

Please explain, I do not understand these problems

Answer 1

Given grammar is

<Z> ::= <L> | <L> <L> | <L> <L> <L>

<L> ::= a | b | c

Here variable <L> generates terminal a ,b, or c.

(i) If we take <Z> ::= <L>

    There will be three sentences {a,b,c}

(ii) If we take <Z> ::= <L> <L>

    There will be 9 sentences , { aa, bb, cc, ab, bc, ca, ba , cb , bc }

(iii) If we take <Z> ::= <L> <L> <L>

      There will be 21 sentences , { aaa , bbb, ccc ,aab ,abc , aca ,aba ,acb ,aac ,abb ,bbc , cba ,bba ,cbb ,abc , acb , bcc ,cca ,bca ,ccb ,acc }

This language contains total of 33 sentences.

Language contains identifier over the input alphabet set { a,b,c} of length at most three.