The minimum number of elements that must be added to relation R = a , b , b , c , b , d on the set a , b , c , d , so that it is an equivalence relation is

Step-by-step solution

Let A = a ,   b ,   c , d ,   R   :   A → A R = a , b , b , c , b , d Reflexive: For reflexivity, we must add a , a ,   b , b ,   c , c ,   d , d Symmetric and Transitive: For symmetric and transitivity, we must add b , a ,   c , b ,   d , b a , c ,   a , d ,   c , d ,   d , c ,   c , a ,   d , a So, we can say that minimum 13 elements are required to make an equivalence relation.