Q$1.$ Consider the following grammar for Boolean expressions.

$EE||E|E$&&$E|!E|(E)|$ bool

bool $$ true $||$ false

a$.$ Show if $!($true $||$ false$)$ is valid.

b$.$ Obtain the rightmost derivation of the string: $!($true $||$ false$)$ &&& $($false$).$

c$.$ Prove that this grammar is ambiguous grammar.

d$.$ Re$-$write this grammar to remove the ambiguity.

e$.$ Eliminate the left recursion in the obtained grammar.

f$.$ Simplify the grammar.

g$.$ Convert the generated grammar in $($f$)$ to Chomsky normal form.

h$.$ Obtain the parse tree for $"!($true $||$ false$)$ && $($false$)"$ using the obtained grammar in $($g$).$