Proving Equivalence Relations: Intersection of Two Sets

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Homework Help Overview

The discussion revolves around set theory, specifically focusing on the properties of equivalence relations and whether the intersection of two equivalence relations is itself an equivalence relation. The original poster seeks to understand how to characterize the equivalence sets resulting from this intersection.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of equivalence relations and the conditions that must be satisfied for a relation to be considered an equivalence relation. Questions are raised about the nature of the intersection of two equivalence relations and whether it meets the necessary criteria.

Discussion Status

The discussion is ongoing, with some participants providing guidance on revisiting definitions and the foundational aspects of equivalence relations. There is an emphasis on understanding the requirements for a relation to qualify as an equivalence relation.

Contextual Notes

Participants note the importance of showing initial attempts and where difficulties arise, in line with forum policies for receiving help.

nishap
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Hi All

I have a problem with Set theory. I am given to prove the following;

Is the intersection of two equivalence relations itself an equivalance relation? If so , how would you characterize the equivalnce sets of the intersection?

Regards,
Nisha.
 
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Hi Nisha,

We have a policy here which is posted at the top of this Forum. In order to receive help, you have to show us how you started and where you got stuck.
 
For any sets A and B, a (binary) relation from A to B is a subset of AxB.

Of what set is an equivalence relation a subset?

What conditions must this subset satisfy?

Since equivalence relations are (sub)sets, the intersection of 2 equivalence relations is a set. Does this set satisfy the conditions required of an equivalence relation?

Regards,
George
 
Just in case you have no clue where to start - going back to the definitions is very helpful.
 

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