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 April 22nd, 2014, 11:39 AM #1 Newbie   Joined: Apr 2014 From: Albany Posts: 1 Thanks: 0 Need help with Equivalence Relation Proof! Let R1 and R2 be equivalence relations on a nonempty set A. A relation R=R1R2 is defined on A as follows: For a,b elements of A, aRb if there exists c element of A such that aR1c and cR2b. Prove or disprove: R is an equivalence relation on A. I am very confused! I know that to show if it is an equivalence relation that I have to show that it is reflexive, symmetric, and transitive. I am just not sure how to go about doing this. Any help would be greatly appreciated. Thanks!
 April 23rd, 2014, 02:42 AM #2 Senior Member     Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra Let $A=\{a,b,c\}$, $R_1 = \{(a,a),\,(a,b),\,(b,a),\,(b,b),\,(c,c)\}$, $R_2 = \{(a,a),\,(b,b),\,(b,c),\,(c,b),\,(c,c)\}$. You can see that $aR_1b$ and $bR_2c$, therefore $aRc$. But does $cRa$? Hence, is $R$ symmetric?

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