Prove that not every finite Partially ordered set can be embedded into $\Bbb R^3$ (ordinary $3$D space) with the partial ordering as follows.
$(x_1,y_1,z_1)\preceq(x_2,y_2,z_2)$ if and only if $(x_1\ge x_2)\land(y_1\ge y_2)\land(z_1\le z_2)$
I don't know how to show that there does not exist such a embedding and how to construct such a set X.