(a) A σ-formula is called universal (resp. existential) if it is of the form x1 x2...x (resp. xx.x,), where is quantifier free. Let A,B be σ-structures with ACB and let p(v) be a σ-formula. Show that for any de A", (i) if op is quantifier free, then A (a) B= (ā); (ii) if op is universal, then Bp(a) ⇒ A = p(a); = (iii) if op is existential, then Ap(a) ⇒ Bo(a). (b) Find a sentence that is true in (N,<) but false in (Z,<).