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.
Solution:
We have,
$R=\{(1,1),(2,2),(3,3),(1,3)\}$
As, $(a, a) \in R$, for all values of $a \in A$
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).