Answered: For each of the following relations ~…

For each of the following relations ~ on sets X, determine whether it is reflexive, symmetric or transitive. Justify all that apply. a) X is the set of positive real numbers and x~y if x2

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 19E: For each of the following relations R defined on the set A of all triangles in a plane, determine...

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Question

For each of the following relations ~ on sets X, determine whether it is reflexive, symmetric or transitive. Justify all that apply.
a) X is the set of positive real numbers and x~y if x²<y²-1

b) X is the set of geometric squares in the plane R², and A~B if A and B both contain the origin.

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