A23 Answer each part for the following context free grammar G l R arrow X R X S S arrow a T b b T a T arrow X T XX X arrow a b a What are the variables of G i True or False T T b What are the...

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A2.3 Answer each part for the following context-free grammar $G$. \[ \begin{array}{l} R \rightarrow X R X \mid S \\ S \rightarrow \mathrm{a} T \mathrm{~b} \mid \mathrm{b} T \mathrm{a} \\ T \rightarrow X T X|X| \varepsilon \\ X \rightarrow \mathrm{a} \mid \mathrm{b} \end{array} \] a. What are the variables of $G$ ? i. True or False: $T \stackrel{*}{\Rightarrow} T$. b. What are the terminals of $G$ ? j. True or False: $X X X \stackrel{*}{\Rightarrow}$ aba. c. Which is the start variable of $G$ ? k. True or False: $X \Rightarrow$ aba. d. Give three strings in $L(G)$. l. True or False: $T \stackrel{*}{\Rightarrow} X X$. e. Give three strings not in $L(G)$. m. True or False: $T \stackrel{*}{\Rightarrow} X X X$. f. True or False: $T \Rightarrow$ aba. n. True or False: $S \stackrel{*}{\Rightarrow} \varepsilon$. g. True or False: $T \stackrel{*}{\Rightarrow}$ aba. o. Give a description in English of h. True or False: $T \Rightarrow T$. $L(G)$.

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#### Solution By Steps ***Step 1: Variables of G*** The variables of G are R, S, T, X. ***Step 2: Terminals of G*** The terminals of G are a, b. ***Step 3: Start Variable of G*** The start variable of G is R. ***Step 4: Strings in L(G)*** Three strings in L(G) are: 1. aaabba 2. bbaaa 3. abba ***Step 5: Strings not in L(G)*** Three strings not in L(G) are: 1. aaaa 2. bbbb 3. ab ***Step 6: Description of L(G)*** The language L(G) consists of strings that can be generated by the grammar G. #### Final Answer a. Variables of G: R, S, T, X b. Terminals of G: a, b c. Start Variable of G: R d. Three strings in L(G): aaabba, bbaaa, abba e. Three strings not in L(G): aaaa, bbbb, ab f. Description of L(G): Language generated by grammar G #### Key Concept Context-Free Grammar #### Key Concept Explanation A context-free grammar consists of a set of production rules that define the language's syntax. It is used to generate strings in a language by applying rules to variables and terminals.

Follow-up Knowledge or Question

What are the variables of a context-free grammar?

What are the terminals of a context-free grammar?

Which is the start variable of a context-free grammar?

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