Let R be a relation over the set N x N and it is defined by (a,b)R(c,d)⇒a+d=b+c Then, R is

We have, (a, b) R (a, b)for all (a,b)∈N×N⇒R is reflexive R is symmetric for we have (a,b)R(c,d)⇒a+d=b+c⇒d+a=c+b⇒c+b=d+a⇒(c,d)R(a,b)Hence, R is symmetric. Then, by definition of R, we have a+ d = b + c and c+ f= d + e hence by addition, we geta+d+ c+ f =b+ c + d+e or a+f =b +e Hence, (a b) R (e, f )Thus, (a, b) R (c, d) and (c, d)R (e, f) ⇒(a, b)R (e f) Hence, R is transitive. Clearly R is equivalence