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Solution


Q.

Let R = {(1, 2), (2, 3), (3, 3)} be a relation defined on the set {1, 2, 3, 4}. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:          [2025]
1 7  
2 10  
3 9  
4 8  

Ans.

(1)

Let A = {1, 2, 3, 4}

R = {(1, 2), (2, 3), (3, 3)}          [Given]

For an equivalence relation 'R' should be reflexive, symmetric and transitive.

∴   Minimum elements that should be added are

(2, 1), (3, 2), (1, 1), (2, 2), (4, 4), (1, 3), (3, 1)

∴   Minimum number of elements required = 7.