# the maximum number of equivalence relations on the set a= {1 , 2 , 3} is

An equivalence relation is one which is reflexive, symmetric and transitive.Given that, A = {1, 2, 3}We can define equivalence relation on A as follows.R1 = A × A = {(1,1),(1,2),(1

An equivalence relation is one which is reflexive, symmetric and transitive.

Given that, A = {1, 2, 3}

We can define equivalence relation on A as follows.

R1 = A × A = {(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),

(3,1),(3,2),(3,3)}

R1 is reflexive (1,1),(2,2),(3,3) R

R1 is symmetric (1,2),(1,3),(2,3) R (2,1),(3,1),(3,2) R

R1 is Transitive (1,2) R and (2,3) R (1,3) R

Similarly,

R2 = {(1,1),(2,2),(3,3),(1,2),(2,1)}

R3 = {(1,1),(2,2),(3,3),(1,3),(3,1)}

R4 = {(1,1),(2,2),(3,3),(2,3),(3,2)}

R5 = {(1,1),(2,2),(3,3)}

maximum number of equivalence relation on A is 5.