The number of equivalence relations that can be defined on set $\{a, b, c\}$, is _____.
Answer & explanation
The number of equivalence relations is 5.
$R_1=\{(a,a),(b,b),(c,c)\}$
$R_2=\{(a,a),(b,b),(c,c),(a,b),(b,a)\}$
$R_3=\{(a,a),(b,b),(c,c),(b,c),(c,b)\}$
$R_4=\{(a,a),(b,b),(c,c),(a,c),(c,a)\}$
$R_5=\{(a,a),(b,b),(c,c),(a,b),(b,c),(c,a),(b,a),(c,b),(a,b)\}$