$10.$ Consider the following expression grammar: Terminals $=\{$num$,+,*,$ $$\}$ Non$-$Terminals $=\{$E$\text{'},$ E$\}$ Rules $=$ E$\text{'}->$ E$; E$->$ num; E$->$ E $+$ E$,$ E $->$ E $*$ EStart Symbol $=$ E$\text{'}$

a$.$ Develop Augmented Grammar

b$.$ Create the LR$(0)$ states and transitions for this grammar

Since this grammar is ambiguous, it is not LR$($k$),$ for any k$.$ We can, however, create a parsetable for the grammar, using precedence rules to determine when to shift, and when to reduce. Assuming that $*$ binds more strongly than $+,$ and both are left$-$ associative, create a parse table using the LR$(0)$ states and transitions. d$.$ Test your parse table with the following strings

C$.$

num $*$ num $+$ num num $+$ num $*$ num num $+$ num $+$ num

e$.$ Now create an LR parse table for this grammar, this time assuming that $+$ binds more strongly than $*,$ and both are right$-$associative. Test your parse table with the followingstrings:

num $*$ num $+$ num num $+$ num $*$ num num $*$ num $*$ num