Question

for the set a={1,2,3} a relation r is defined as r={(1,1),(2,2),(3,3),(1,3)}. write the ordered pairs to be added to R to make the smallest equivalence relation.

Answer 1

An equivalence relation must be reflexive,symmetric and transitive.
(1,1),(2,2),(3,3) -∴R is reflexive
for(1,3) there must be a (3,1) in the relation for be a symmetric(for all (a,b) there must be (b,c))
transitive -if there is (a,b) and (b,c) then there must be (a,c)
for (1,1) and (1,3) there is (1,3)
for (3,3) and (3,1) there is (3,1)
Hence, when (3,1) is in the relation then the relation is equivalence.So(3,1) is the ordered pair.