Prove that certain sets are not convex. For each of the following sets, give the coordinates of
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Question:
Prove that certain sets are not convex. For each of the following sets, give the coordinates of two points where P and Q are in the set, but the line from P to Q goes outside the set.
(a) R = {(x , y ): x 2 + y 2 ≥ 1, y<0}
(b) S = {(x , y ): (x - 1) 2 + y 2 ≤ 1} ∪ {(x , y ): (x + 1) 2 + y 2 ≤ 1}
(c) T = {(x , y ): x 2 >2} ∩ {(x , y ): y 2 <4}
Related Book For
Discrete Mathematics and Its Applications
ISBN: 978-0073383095
7th edition
Authors: Kenneth H. Rosen
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