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Solution


Q.

If R is the smallest equivalence relation on the set {1, 2, 3, 4} such that {(1,2),(1,3)}⊂R, then the number of elements in R is _______ .             [2024]
1 12  
2 15  
3 10  
4 8  

Ans.

(3)

   To make R an equivalence relation, R should be reflexive, symmetric, and transitive.

   ∴ R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (1,3), (3,1), (3,2), (2,3)}

   So, minimum number of elements in R should be 10.