Provide an example of a context$-$free grammar over the alphabet $\{$a$,$ b$,$ c$,$ d$,$ e$\},$ which meets all the following properties:

The grammar is SLR$(1).$

There is a word on which an SLR$(1)$ parser will perform reductions before it discovers the error, while an LALR$(1)$ parser will immediately detect the error.

There is a word on which an LALR$(1)$ parser will perform reductions before it discovers the error, while a canonical LR$(1)$ parser will immediately detect the error.

In your answer:

a$.$ Present the grammar.

b$.$ Construct the LR$(0)$ item automaton of the extended grammar.