Mathematics Behind Simplex Method |Part 4| Some Basic results on Convex sets

In this video, I have proved some basic results on Convex sets. 1. The Union of two convex sets is not convex (counter example is given), 2. Intersection of two convex sets is convex. 3. Polyhedron which is Intersection of hyperplanes/half Planes is convex; Feasible Region is convex set. Mathematics Behind Simplex Method |Part 3|:    • Mathematics Behind Simplex Method |Part 3|...   Mathematics Behind Simplex Method |Part 2|:    • Mathematics Behind Simplex Method |Part-2|...   Mathematics Behind Simplex Method |Part 1|:    • Mathematics Behind Simplex Method |Part-1|...   The reason of why we can always find the optimal solution at corner point is the Fundamental Theorem of LPP, and to prove this theorem we need the assumption that the feasible region is a Convex Set/Convex Polyhedron. So by proving that Feasible region is Convex Polyhedron we present a Pre-requisite condition to Fundamental Theorem of LPP.