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Equivalence Relations 
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#1
Apr2714, 05:39 PM

P: 38

Hi,
I'm reading a book on sets and it mentions a set B = {1,2,3,4} and it says that R3 = {(x, y) : x ∈ B ∧y ∈ B} What does that mean? Does that mean every possible combination in the set? Also the book doesn't clarify this completely but for example using the set B say i had another set R = {(1,2),(2,3),(1,3),(1,1),(2,2),(3,3),(4,4)}, Would this be clarified as transitive and reflexive? My question is does a set need to have all transitive properties and all the reflexive properties to be called transitive and reflexive. If i had another set: R1 = {(1,2),(2,3),(1,3),(1,1),(2,2),(3,3)} In which i removed (4,4) would this set R1 still be considered reflexive? Thanks in advance 


#2
Apr2714, 05:58 PM

Sci Advisor
P: 1,807

Your first example is a transitive and reflexive relation. A relation is transitive and reflexive if it satisfies the axioms for transitivity and reflexivity.
Your other example is not reflexive, since 4 is an element of X, but 4 ~ 4 is not satisfied. 


#3
Apr2814, 08:44 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,553




#4
Apr2814, 08:56 AM

P: 38

Equivalence Relations
Ahh, thanks!!! This helped me understand it a lot better



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