Question

1. Draw a convex set S. Explain briefly how you know S is convex. Then break that set into two sets Sį and S2 such that Si U S2 = S and Sin S2 = 0 and neither Si nor S2 is convex. 2. Consider a sphere S. Lines on the sphere are taken to be great circles. On the sphere, does the Plane Separation Postulate hold? Give a short explanation to back up your claim that considers the various parts of the Plane Separation Postulate.

Answer 1

Conne sedi A set s is said to be conebs get if a line joined between any two points of the set is completely be on that set. S2 22 S2 Here se includes boundary Si from every s hut S2 does not includes boundary from upper part clearly, Sis a connex set, as we can join a live between too points from the set and the line is completly be in s. But neither Si nos. Se are Conces sets as we can see that in so have joined a line between on, and y, that does not completely lies we have doain a line inside se between and 2 that also does not completely lies in Sri thor Also Susa – S and sins. 28. And sis connea set where neithes Si nos Se are connex set. wei inside Sio similarly nr

Crowe sedi A set s is said to be connes set if a line joined between any two points of the set is completely be on that set. from every a line n2 S2 Here se includes boundary Si where, S₂ but S2 does not includes boundary from upper part Clearly, S is a connex set, as we ean join between any too points from the set and the line is completly lies in s. Convex sets as But neither Si nos. Su are we can see that in si have joined between on, and y, that does not completely lies inside Sue similarly have dzawn a line inside Sy between and Я that also does not completely lies in Sri Hercoss Also, Suszas and Sin S2 28. And sis connea set where neithes S. nor Se are connex seta a line 92
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