The maximum number of equivalence relations on the set A = {a, b, c} is:

5

The correct answer is Option (3) → 5

equivalence relations possible sets

$R_1= \{(a,a),(b,b),(c,c)\}$

$R_2= \{(a,a),(b,b),(c,c),(a,b),(b,a)\}$

$R_3= \{(a,a),(b,b),(c,c),(b,c),(c,a)\}$

$R_4= \{(a,a),(b,b),(c,c),(a,c),(c,a)\}$

$R_5= \{(a,a),(b,b),(c,c),(a,b),(b,a),(a,c),(c,a),(b,c),(c,b)\}$

 No. of equivalence relations = 5