(a) (1) Let po, P1.90, 91, 90, 1 be atoms capturing the states of three cells called p, q, and r, that can each either hold a 0 or a 1: p; captures the fact that cell p holds the value i, and similarly for the other atoms. Consider the following formula: (P. V p.) ^ (90 V91) ^ (ro Vr1)^(-po V-2)^(-90 V-91)^(-V-) A(po V90 V ro) (P1 V 4.) ^ (P1 Vra) A(91 Vr) Using DPLL, prove whether the above formula is satisfiable or not. Detail your answer. What property of the three cells p, q, and r, is this formula capturing? [4 marks] (ii) Given a CNF (Conjunctive Normal Form) that contains a clause composed of a single literal, can it be proved using Natural Deduction? Justify your answer. [2 marks]