Problem 1 Let L = {P, Q} where P and Q are unary relation symbols. Consider the following rst order theory, T, consisting of the following sentences: (1) WWW VQ($))- (2) For every n > 2, _as1..._:cn /\\ mi % 5133' /\\ A (POW) A "Q($i)) 152',an 1991 iii (3) For every n > 2, Elm]...E|;r:,, /\\ as, 7 arj /\\ A (Q(m,) /\\ -IP(;r,)) 19',an igign Iii (4) For every n > 2, 3931-390, /\\ mmjxx /\\ (Pm/mm 19,an igign isj Part 1: Give an example M of a model of T Where M = (N, PM,QM). Notice that you need to give PM and QM. Part 2: Sow that any two countable models of T are isomorphic. Possible Hint: An easy way to think about models of T is to draw two ovals. Part 3: Deduce that T is complete. State any theorems from class which you use