Consider the formula$($In picture$)(($PQ$)$R$)($P$($QR$))($a$)$ Prove the validity of the above formula using rules of natural deduc$-$tion$($b$)$ Prove the validity of the above formula using semantic tableaux. Do not convert the formula into CNF form, directly apply the $,$ rule $($a$,$b rule, alpha beta rule$)2.$ For the same formula from question $1($a$)$ Convert the negation of the given formula into CNF form$($b$)$ Convert the CNF formula obtained in a$)$ into clausal form$($c$)$ Use resolution refutation procedure on the clausal form obtained in b$)$ to derive false.Show all working mathematically and break it down into steps, then show the correct answer at the end. Consider the formula $((P^{{?}^{?}}Q)R)(P(QR))$