21 •Show that the subsets of the plane are open.18.) A = {(x,y) -1 < x < 1₁ -1 < y ≤1}19.) B= {(x, y²ly >0}| 20.1 C = {(x₁y) |2 < x² + y ² <4}21.) 0= {(x, y) / x +0 andy +0}

Answered: 21.) 0= {(x, y)/x +0 andy +0 } D=

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21.) 0= {(x, y)/x +0 andy +0 } D=

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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Question

•Show that the subsets of the plane are open.
18.) A = {(x,y) -1 < x < 1₁ -1 < y ≤1}
19.) B= {(x, y²ly >0}
| 20.1 C = {(x₁y) |2 < x² + y ² <4}
21.) 0= {(x, y) / x +0 andy +0}

Expert Solution

Step 1

We have result that a set is open if and only if its complement is closed. So we will use this result here.

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