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Equivalence Relations!

  • Thread starter ragnes
  • Start date
  • #1
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1. Let R be a relation on X that satisfies
a) for all a in X, (a,a) is in R
b) for a,b,c in X, if (a,b) and (b,c) in R, then (c,a) in R.
Show that R is an equivalence relation.




2. In order for R to be an equivalence relation, the following must be true:
1) for all a in X, (a,a) is in R
2) for a,b in X, if (a,b) is in R, then (b,a) is also in R
3) for a,b,c in X, if (a,b) and (b,c) is in R, then (a,c) is in R.




3. The first part is given by the definition of an equivalence relation. I'm stuck on proving part b. Help please!

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
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how about considering (a,b) and (b,b) for the second part?
 
  • #3
115
1
how about considering (a,b) and (b,b) for the second part?
Proof by contradiction, using lanedance's example.

Or consider (b,c) and (c,c).
 

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