Let A = 1, 2, 3, 4, 5 and R be a relation on A defined as R = (1,2), (2,3), (4,5) . The minimum number of ordered pairs that must be added to R so that the enlarged relation becomes an equivalence relation is :

Step-by-step solution

An equivalence relation on a set partitions the set into disjoint equivalence classes. The given relation is R = (1,2), (2,3), (4,5) . For the enlarged relation to be an equivalence relation, it must be reflexive, symmetric, and transitive. The presence of (1,2) and (2,3) implies that 1, 2, and 3 must belong to the same equivalence class. The presence of (4,5) implies that 4 and 5 must belong to the same equivalence class. To minimize the number of ordered pairs in the equivalence relation, we should not merge thes