Question

Let B be the language of properly nested parentheses and brackets. For

example, ( [()()]()[] is in B but ([]\right. is not. Show that B is in
L .

Answer 1

To show that the language B of properly nested parentheses and brackets is in L, we can define a context-free grammar (CFG) for B.

Step-by-step explanation:

To show that the language B of properly nested parentheses and brackets is in L, we can define a context-free grammar (CFG) for B. Here is an example of such a CFG:

S → SS
S → (S)
S → [S]
S →ε

This CFG generates strings that consist of properly nested parentheses and brackets. By definition, context-free grammars generate context-free languages, and therefore, B is in L.

To show that the language B of properly nested parentheses and brackets is in L, we can define a context-free grammar (CFG) for B.