Q2 R={(a.o) €Ax Alpe 사}.In other words, R is the diagonal in A x A.Note: The hypotheses here are a little different from what was stated in class. Thecontainment {(a, a) E A x Ala E A} C R follows from the fact that R is reflexive.The containment RC {(a, a) E Ax Ala E A} will take more work and uses the other2 properties.2. Define~ on R? by (x, y)(u, v) if and only if x2 + y? = u² + v². In class, we saw%Dthat this defines a binary relation on R2 which is reflexive, symmetric, and transitive,hence it is an equivalence relation. Describe all of its equivalence classes.

Answered: Image /qna-images/answer/b527761a-2f7c-4265-a7b0-e383ce47e3ba.jpg

~ on R? by (x, y) ~ (u, v) if and only if ? + y? = u² + v2. In class, we saw that this defines a binary relation on R2 which is reflexive, symmetric, and transitive, hence it is an equivalence relation. Describe all of its equivalence classes. Define

~ on R? by (x, y) ~ (u, v) if and only if ? + y? = u² + v2. In class, we saw that this defines a binary relation on R2 which is reflexive, symmetric, and transitive, hence it is an equivalence relation. Describe all of its equivalence classes. Define

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 24E: The Segment-Addition Postulate can be generalized as follows: The length of a line segment equals...

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Question

R={(a.o) €Ax Alpe 사}.
In other words, R is the diagonal in A x A.
Note: The hypotheses here are a little different from what was stated in class. The
containment {(a, a) E A x Ala E A} C R follows from the fact that R is reflexive.
The containment RC {(a, a) E Ax Ala E A} will take more work and uses the other
2 properties.
2. Define
~ on R? by (x, y)
(u, v) if and only if x2 + y? = u² + v². In class, we saw
%D
that this defines a binary relation on R2 which is reflexive, symmetric, and transitive,
hence it is an equivalence relation. Describe all of its equivalence classes.

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