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For x, Y E JR, let X ~ Y mean that xy > O. Which properties of an equivalence relation

Chapter 9, Problem 9.9

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QUESTION:

For x, Y E JR, let X ~ Y mean that xy > O. Which properties of an equivalence relation does ~satisfy? Answer the same question with X Y ~ 0 in place of.xy > O.

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QUESTION:

For x, Y E JR, let X ~ Y mean that xy > O. Which properties of an equivalence relation does ~satisfy? Answer the same question with X Y ~ 0 in place of.xy > O.

ANSWER:

Step 1 of 3

For the, let  such that .

Consider that  and . This suggest that  is not reflexive.

Consider that  then, . The product on  is commutative and xy=yz. It can be concluded that yx>0 and  have  as symmetric.

 

 

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