(a) Show that the following sets are not convex:i. S = {x € R²: x² = x² + x₁ + x₂ ≤ 4}.-ii. T{x € R²: x²-x² + x₁ + x₂ ≥ 4}.=(b) Let C be a convex set.Prove that x ES is an extreme point of C if and only if C - {x} is convex.

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(a) Show that the following sets are not convex: - i. S = {x € R²: x² = x² + x₁ + x₂ ≤ 4}. ii. T = {x € R²: x²-x² + x₁ + x₂ ≥ 4}.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.4: Relationships: Perpendicular Lines

Problem 18E: Does the relation is a friend of have a reflexive property consider one person? A symmetric property...

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Question

(a) Show that the following sets are not convex:
i. S = {x € R²: x² = x² + x₁ + x₂ ≤ 4}.
-
ii. T
{x € R²: x²-x² + x₁ + x₂ ≥ 4}.
=
(b) Let C be a convex set.
Prove that x ES is an extreme point of C if and only if C - {x} is convex.

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