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Question
For the set A = {1, 2, 3}, define a relation R on the set A as follows:
R = {(1, 1), (2, 2), (3, 3), (1, 3)}
Write the ordered pairs to be added to R to make the smallest equivalence relation.
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Solution
We have,
R = { (1, 1), (2, 2), (3, 3), (1, 3) }
As, (a, a) ∈ R, for all values of a∈ A
So, R is a reflexive relation
R can be a symmetric and transitive relation only when element (3, 1) is added
Hence, the ordered pairs to be added to R to make the smallest equivalence relation is (3, 1).
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