Michael Sipser Edition 3 Exercise 2 Question 3 (Page No. 155)

Question

Answer each part for the following context-free grammar $G.$
                           $R\rightarrow XRX | S$
                           $S\rightarrow aT b | bT a$
                           $T\rightarrow XT X | X | \epsilon$
                          $X\rightarrow a | b$

1. What are the variables of $G?$
2. What are the terminals of $G?$
3. Which is the start variable of $G?$
4. Give three strings in $L(G).$
5. Give three strings not in $L(G).$
6. True or False$:T\Rightarrow aba.$
7. True or False$:T \overset{*}{\Rightarrow}aba.$
8. True or False$:T\Rightarrow T.$
9. True or False$:T\overset{*}{\Rightarrow}T.$
10. True or False$: XXX\overset{*}{\Rightarrow}aba.$
11. True or False$:X\overset{*}{\Rightarrow}aba.$
12. True or False$:T\overset{*}{\Rightarrow}XX.$
13. True or False$:T\overset{*}{\Rightarrow}XXX.$
14. True or False$:S\overset{*}{\Rightarrow}\epsilon.$
15. Give a description in English of $L(G).$