A subset S of a plane satisfying incidence and betweenness axioms is called convex if for any two points X,Y in S the whole segment XY is contained in S Recall that the side of any line is a convex set. (a) Prove that intersection of (any family of) convex sets is convex (b) Prove that any ray is a convex set. (c) Prove that a segment, an interior of an angle, an interior of a triangle are (use a) and b)) convex

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