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Solution


Q.

The minimum number of elements that must be added to the relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d} so that it is an equivalence relation is _____________ .    [2023]

Ans.

(13)

Given S={(a,b),(b,c),(b,d)}

Reflexive:(a,a),(b,b),(c,c),(d,d)Symmetric:(b,a),(c,b),(d,b)Transitive:(a,c),(a,d),(d,c)↓↓↓(c,a)(d,a)(c,d)

So, 13 elements must be added.