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~ 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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
Transcribed Image Text: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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