Question $4$: $(20$ points$)$

Consider the following grammar:

E$->$E$+$T$|$T

T$->$T$*$F$|$F

F$->($E$)|$ id

In class, we used an LR parser to shift and reduce the following expression $"$id $+$ id $*$ id$".$

a$)$ Can you use the current grammar with an LL$(1)$ parser for the expression $$id $+$ id $*$ id$?$ Explain your answer.

b$)$ If LL$(1)$ parser can$$t be used fix the grammar $($also show the fixed grammar$)$ and show your parse tree. If grammar doesn$$t need to be fixed, only show the parse tree.