I am facing the problem of the linear separability of a three dimensional cube.
Let's take the opposite vertexes of the cube as $(0, 0, 0), (1, 1, 1)$. It is possible to split it with a plane in two tetrahedron-like parts, and so define two sets, each containing lying points lying on a specific side of the plane. Let's take one of the set $t=\{(0, 1, 1), (1, 1, 1), (1, 0, 1), (1, 1, 0)\}$ and the other the obvious complement.The question is: what is the simplest form of the boolean function $P$ such that $\forall x \in t: P(x)=1$?