The number of equivalence relations that can be defined on set $\{a, b, c\}$, is _____.

5

The number of equivalence relations is 5. $R_1=\{(a,a),(b,b),(c,c)\}$ $R_2=\{(a,a),(b,b),(c,c),(a,b),(b,a)\}$ $R_3=\{(a,a),(b,b),(c,c),(b,c),(c,b)\}$ $R_4=\{(a,a),(b,b),(c,c),(a,c),(c,a)\}$ $R_5=\{(a,a),(b,b),(c,c),(a,b),(b,c),(c,a),(b,a),(c,b),(a,b)\}$