Question

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

Answer 1

This is your answer...
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Answer 2

given: A ={1, 2, 3} .

to find: the smallest equivalence relation R on set A

1. An equivalence relation is a relationship on a set,   generally denoted by “∼”.

2. That is reflexive, symmetric, and transitive for everything in the set.  

3. Example: The relation “is equal to”, denoted “=”, is an equivalence relation on the set of real numbers since for any x, y, z ∈ R: 1.

So the equivalence relation on set A is

{1,1}, {1,2}, {1,3}, {2,1}, {2,2}, {2,3}, {3,1}, {3,2},{3,3}