Proving Equivalence Relations: Intersection of Two Sets

AI Thread Summary
The discussion centers around proving whether the intersection of two equivalence relations is itself an equivalence relation. Participants emphasize the importance of understanding the definitions and conditions that define equivalence relations. It is noted that the intersection of two equivalence relations forms a set, but the key question is whether this set meets the necessary criteria for being an equivalence relation. The conversation encourages showing initial work to facilitate assistance. Overall, the focus is on the foundational principles of set theory and equivalence relations.
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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