$(20$ points$)$ Convert the following grammar to $LL(1)$ form by eliminating left recursion $($B$,T$ and $C$ are

non$-$terminals. or$,$ and, not, true, false, $(,$ and $)$ are terminals.$)$ Show that the converted grammar

is $LL(1)$ by

$($a$)$ calculating the first set and follow set for each non$-$terminal,

$($b$)$ calculating the predict set for each rule,

$($c$)$ constructing the $LL(1)$ parse table,

$($d$)$ and identifying if there exist conflicts in the parse table,