12.18

The next three exercises contain arguments from a single set of premises. In each case decide whether or not the argument is valid. If it is, give an informal proof. If it isn't, use Tarski's World to construct a counterexample. 12.16 |yxty [LeftOf(x,y) Larger(x, y)] 11 )] yx[Cube(x) Small(x yx Tet(x) Large(x)] yxty (Small (x) Small (y)) -Larger (x, y)| -3x3x [Cube(x) Cube(y) RightOf(x,y)) 12.17 lyxVyLeftOf(x,y) Larger(x,y)] | yx Cube(x) Small(x)) yx Tet(x) Large(x)] yxty (Small (x) Small (y)) Larger (x, y)| Vz Medium(z) Tete) 12.18 .lea |YxVyLeftOf(x,y)Larger(x,y)] | )] yx[Cube(x) Small(x yx Tet(x) Large(x)| yxty (Small (x) Small (y)) -Larger (x, y)| VzYw(Tet(z) Cube(w)) LeftOf(z, w)] The next three exercises contain arguments from a single set of premises. In each case decide whether or not the argument is valid. If it is, give an informal proof. If it isn't, use Tarski's World to construct a counterexample. 12.16 |yxty [LeftOf(x,y) Larger(x, y)] 11 )] yx[Cube(x) Small(x yx Tet(x) Large(x)] yxty (Small (x) Small (y)) -Larger (x, y)| -3x3x [Cube(x) Cube(y) RightOf(x,y)) 12.17 lyxVyLeftOf(x,y) Larger(x,y)] | yx Cube(x) Small(x)) yx Tet(x) Large(x)] yxty (Small (x) Small (y)) Larger (x, y)| Vz Medium(z) Tete) 12.18 .lea |YxVyLeftOf(x,y)Larger(x,y)] | )] yx[Cube(x) Small(x yx Tet(x) Large(x)| yxty (Small (x) Small (y)) -Larger (x, y)| VzYw(Tet(z) Cube(w)) LeftOf(z, w)]