The minimum number of elements that must be added to the relation R={(1,2),(2,3)} on the sub set {1,2,3} of natural numbers so that it is an equivalence relation is

R is reflexive if (x,x)∈R for all x∈{1,2,3}⇒  (1,1),(2,2),(3,3)∈RR is symmetric if (1,2),(2,3)∈R⇒  (1,3)∈R also (3,1)∈R as R is transitive if (1,2),(2,3)∈R⇒  (1,3)∈R  also (3,1)∈R as R is symmetric.So the total numbers of elements is 9.