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

Question

Philoid · Accepted Answer

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