The maximum number of equivalence relations on the set A = {a, b, c} is:
Answer & explanation
Correct answer: option 3
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