A=1,2,3...9RinA×A(a,b)R(c,d)if(a,b)(c,d)∈A∈Aa+b=b+cConsider(a,b)R(a,b)(a,b)∈A×Aa+b=b+aHence,Ris reflexive.Consider(a,b)R(c,d)given by(a,b)(c,d)∈A×Aa+d=b+c=>c+b=d+a⇒(c,d)R(a,b)HenceRis symmetric.Let(a,b)R(c,d)and(c,d)R(e,f)(a,b),(c,d),(e,f),∈A×Aa+b=b+candc+f=d+ea+b=b+c⇒a−c=b−d– (1)c+f=d+e– (2)Adding (1) and (2)a−c+c+f=b−d+d+ea+f=b+e(a,b)R(e,f)Ris transitive.Ris an equivalence relation.We select from setA=1,2,3,9aandbsuch that2+b=5+asob=a+3Consider(1,4)(2,5)R(1,4)⇒2+4=5+1[(2,5)=(1,4)(2,5),(3,6),(4,7),(5,8),(6,9)]is the equivalent class under relationR.