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.

Question

Philoid · Accepted Answer

Given set A = {1, 2, 3} and relation R = {(1, 1), (2, 2), (3, 3), (1, 3)}

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

⇒ R = {(1, 1), (2, 2), (3, 3), (1, 3)} is reflexive and transitive but not symmetric.

⇒ If (3,1) is added to the ordered pairs, R will become symmetric.

Thus the new R:

⇒ R = {(1, 1), (2, 2), (3, 3), (1, 3),(3,1)} is the obtained smallest equivalence relation.

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.

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.