# Math forum

 Sets and Relations Options
shine123
 #1 Posted : Monday, May 07, 2012 11:54:37 AM
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Let R be the relation on the set of real numbers defined by x R y  iff  x-y is a  rational number . Determine whether R is reflexive , symmetric , antisymmetric and /or transitive

brosnan123
 #2 Posted : Friday, September 06, 2013 10:30:07 AM

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Solution :

Given  x-y rational numberreflexive (x-x=0 is rational ) symmetric (x-y rational => y-x rational ) not a antisymmetric ( 1-2 rational ,2-1 rational ,2≠1 ) transitive (x-y rational and y-z rational implies x-z=x-y+y-z rational)

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