Chapter 8.5, Problem 17E

In Exercises 16 and 17, mark each statement True or False. Justify each answer.

17.

1. a. A cube in ℝ³ has exactly five facets.
2. b. A point p is an extreme point of a poly tope P if and only if p is a vertex of P.
3. c. If S is a nonempty compact convex set and a linear functional attains its maximum at a point p, then p is an extreme point of S.
4. d. A 2-dimensional polytope always has the same number of vertices and edges.