- #1
nikie1o2
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In R x R , ley (x,y) R (u,v) if ax^2 +by^2=au^2 + bv^2, where a,b >0. Determine the relation R is an equivalnce relation. Prove or give a counter example
Is R an Equivalence Relation in R x R Based on a Quadratic Equation?
- Thread starter nikie1o2
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- Equivalence Proof Relation
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Homework Help Overview
The discussion revolves around determining whether a specific relation R defined on R x R, based on a quadratic equation, is an equivalence relation. The original poster seeks to prove or provide a counterexample regarding the reflexive, symmetric, and transitive properties of this relation.
Discussion Character
- Conceptual clarification, Assumption checking, Mathematical reasoning
Approaches and Questions Raised
- The original poster attempts to establish the properties of reflexivity, symmetry, and transitivity for the relation R, expressing confusion about how to demonstrate these properties in the context of four variables. Some participants suggest clarifying definitions and writing out the equations to aid understanding.
Discussion Status
Participants are engaged in exploring the properties of the relation R, with some providing guidance on how to approach the proof. There is an ongoing discussion about variable naming conventions and their implications for clarity in the problem.
Contextual Notes
There is a note from a moderator regarding the appropriate forum for posting homework assignments, indicating that the discussion may be part of an assigned coursework or independent study. The original poster expresses prior experience with equivalence relations but indicates uncertainty due to the complexity introduced by the quadratic equation involving four variables.
- #2
tiny-tim
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Welcome to PF!
Hi nikie1o2! Welcome to PF!
(try using the X2 tag just above the Reply box
)
Tell us how far you've got, and where you're stuck, and then we'll know how to help!
Hi nikie1o2! Welcome to PF!
(try using the X2 tag just above the Reply box
)Tell us how far you've got, and where you're stuck, and then we'll know how to help!
- #3
nikie1o2
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tiny-tim said:Hi nikie1o2! Welcome to PF!
(try using the X2 tag just above the Reply box
Tell us how far you've got, and where you're stuck, and then we'll know how to help!
Hello, thank you for the warm welcome.
I have done equivalence relations before but with just two variables not 4. So i was confused on how to prove the reflexive, symmetric & transitive properties.
For reflexive i was thinking if (x,y)R(x,y) then ax^2+by^2=ax^2+by^2- so that is true
Symmetry: (x,y)R(u,v) then (u,v)R(x,y) is true
For Transitive i knoe if(x,y)R(u,v) and (u,v)R(a,b), then (x,y)R(a,b). I am just confused on how to show the equations for that and that it's true...
- #4
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- #5
tiny-tim
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Hello nikie1o2!
(Please use the X2 tag just above the Reply box)
Just write out the definitions of (x,y)R(u,v) and (u,v)R(a,b) … then it should be obvious!
(btw, the equivalence classes are a well-known geometrical shape … can you se which?)
(Please use the X2 tag just above the Reply box
)nikie1o2 said:
Just write out the definitions of (x,y)R(u,v) and (u,v)R(a,b) … then it should be obvious!
(btw, the equivalence classes are a well-known geometrical shape … can you se which?)
- #6
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- 186
Just a comment: using "a" and "b" is a bad choice of variable names in this problem. May I suggest using "s" and "t" instead? I.e., use
(u,v)R(s,t)
instead of(u,v)R(a,b)
when working out the transitive property.Similar threads
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