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Let A = 1 , 2 , 3 , 4 and R = ( 1 , 2 ) , ( 2 , 3 ) , ( 1 , 4 ) be a relation on A . Let S be the equivalence relation on A such that R ⊂ S and the number of elements in S is n . Then, the minimum value of n is _______

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Given, A = 1 , 2 , 3 , 4 and R = ( 1 , 2 ) , ( 2 , 3 ) , ( 1 , 4 ) be a relation on A . Now, given S be the equivalence relation on A and R ⊂ S So, for S to be equivalence it should be Reflexive, Symmetric and Transitive on given relation, Now, for reflexive Relation we need, 1 , 1 , 2 , 2 , 3 , 3 , 4 , 4 → 4 elements, For Symmetric relation we need, 2 , 1 , 3 , 2 , 4 , 1 → 3 elements, And for Transitive relation we need, 1 , 3 , 3 , 1 , 3 , 4 , 4 , 2 , 2 , 4 , 4 , 3 → 6 elements So, minimum 13 elements should be a

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