(a,b)R(c,d)⟺a+b=b+c a+a=a+a ⇒(a,a)R(a,a)⟹R is reflexive Next,Let (a,b)R(c,d)⇒a+b=b+c ⇒c+b=d+a⇒(c,d)R(a,b) ⟹ R is symmetric Next,(a b) R (c,d) and (c,d) R (e,f) ⇒a+b=b+c and c+f=d+e ⇒a+d+c+f=b+c+d+e ⇒a+f=b+e⇒(a,b)R(e,f) ⟹ R is transitive ⟹ R is an equivalence relation.