Q24 of 109 Page 1

Write the smallest equivalence relation on the set A = {1, 2, 3}.

A relation is an equivalence relation if and only if it is reflexive, symmetric and transitive:


The smallest equivalence relation on the set A={1,2,3} is :


R={(1,1),(1,3),(3,1)}


∵ (1,1) ∈ R → Reflexive


(1,3) ∈ R and (3,1) ∈ R → Symmetric


(1,3) ∈ R and (3,1) ∈ R and (1,1) ∈ R → Transitive


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