The grammar BP $=(\{(,)\},\{$S$\},\{$S $->\backslash$lambda $|$ SS $|($S$)\},$ S$)$ generates the

language of balanced parentheses, that is words like $()$ and $(())(),$ but not $)$ and $(().$

$1.$ Use the rules of BP to generate the word $(())().$ Show clearly all the steps of the generation.

$2.$ Use BP as a guide to write a grammar that generates the language of two types of balanced

parentheses such as $()\{\}$ and $(\{\}()).$ The alphabet in this case consists of the four symbols

$(,),\{,\}.$