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3. Take the set S = {(1,5),(5,1),(4,4),(0,0)) cR^2, where R^2 is a so-called Cartesian Product.' a) Plot the set. b) Is the set convex? If yes, explain why. If no, explain how you could convexify the set, what the smallest convexification would be (if that exists), and indicate it in your graph.

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steffaniasierrag

Answer:

a) The first image is the plot of the set S. The plot correspond only to the four points.

b) The set is not convex because the points that lies in the segment between (1,5) and (5,1) doesn't belong to the set.

The set can be convexifies adding the linear combinations of the points of S.

The graph of smallest convexification of the set is in the second image that correspond to the polygon with vertices (1,5),(5,1),(4,4),(0,0).

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