Exercise 4.9. Suppose x, y E R and assume that x

Exercise 4.9. Suppose x, y IR and assume that a; < y. Show that for all z (a; y), there exists a e (0, 1) so that ax + (1 -- a)y = z. Now, also prove that a set X C IR is convex if and only if the set X satisfies the property that for all x, y e X, with < y, for all z e G, y), z G X.