$(30$pt$)$ Consider Boolean expressions containing operands $($id$),$ operators $($and$,$ or$),$ and parentheses,

where and has higher precedence than or$.$

$($a$)(10$pt$)$ Write an SLR$(1)$ grammar, $G,$ which is not LL$(1),$ for such expressions, which obeys the

precedences indicated.

$($b$)(5$pt$)$ Compute the First$(x)$ and FOllow$(x)$ sets for all nonterminals $x$ and PrEdiCt$(i)$ sets for

all productions $i.$

$($c$)(5$pt$)$ Prove that $G$ is not $LL(1).$

$($d$)(10$pt$)$ Prove that $G$ is SLR$(1)$ by drawing the SLR graph and show there are no conflicts. Build the

graph as shown in the examples we did in class $($and done by jflap$),$ not the condensed form in the

textbook. For each state with potential conflicts $($two LR$-$items, one with the dot in the middle, one

with the dot at the end$),$ explain clearly why there is no shift$/$reduce conflict.