Consider the following grammar for Boolean expressions. S+S OPS!S(S) t|f OP ||| && a. Show if !(t && f) is valid. b. Obtain the rightmost derivation of the string: (t || f) && !(f) 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. Obtain the parse tree for the string" (f || t) && !(t)