In the book of Richard Hammack, I come accross with the following question:
There are two diļ¬erent equivalence relations on the set $A = \{a,b\}$. Describe them.
OK, I found that the solution is,
$R_1 = \{(a,a),(b,b),(a,b),(b,a)$ and $R_2 = \{(a,a),(b,b)\}$
Then I thought two more equivalence classes $R_3 = \{(a,a)\}$, $R_4 = \{(b,b)\}$. But when I looked the answer, I saw that, $R_1$ and $R_2$ are true but others are false. Why is that?