4. a) Let X=RR. For each (a,b)X, let D(s,b={(x,y)X:x=a}{(x,y)X:x2+y2=a2+b2} Is {D(a,b):(a,b)X} a partition of X ? Prove your answer. b) Define a relation R on X by (x,y)R(u,D) if and only if there exists a member D(a,b) of {Da,b):(a,b)X} such that (x,y) and (a,b) both belong to D(a,b). Is R refluxive on X2 ? symmetric? transitive? In each case, prove your