Let R be a relation over the set N×N and it is defined by a, bRc, d⇒a+d=b+c. Then R is

We have a, bR(a, b) for all (a, b)∈N×NSince a+b=b+a. Hence, 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(e,f).Then by definition of R, we havea+d=b+c and c+f=d+e,whence by addition, we geta+d+c+f=b+c+d+e or a+f=b+eHence, (a,b)R(e,f)Thus, (a, b)R(c, d) and (c, d)R(e,f)⇒(a, b)R(e, f).