- Consider Universe U 0 0 Where We Have A Single Unary Function F A Unary Predicate P And A Single Constant A As 1 (163.34 KiB) Viewed 40 times
Consider universe U = {0,0,*}, where we have a single unary function f, a unary predicate p, and a single constant a. Assume, we have variable assignment o(x) = * and the following interpretation: l(a) = 0 = l(f) = {*+0, 0+0,0→*} = l(p) = {{*, O), (0, 0), = 0), (0, 0)} Now consider formulas F = p(x, a) → p(f(x), a) G = 3x.( p(x, x) → p(x, f(x))) Let S = (U, I). Which of the following statements is true C S, O F F and S, O F G, that is, both F and G are true. S, OFF and S, O # G, that is, F is true, but G is not true. C S, O # F and S, O F G, that is, F is not true, but G is true. OS, O # F and S, o # G that is, neither Fnor G are true.