The maximum number of equivalence relations on the set $A = \{1, 2, 3\}$ are

5

The correct answer is Option (4) → 5 ##

Given that, $A = \{1, 2, 3\}$

Now, number of equivalence relations as follows.

$R_1 = \{(1, 1), (2, 2), (3, 3)\}$

$R_2 = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)\}$

$R_3 = \{(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)\}$

$R_4 = \{(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)\}$

$R_5 = \{(1, 2, 3) \Leftrightarrow A \times A = A^2\}$

$∴$ Maximum number of equivalence relation on the set $A = \{1, 2, 3\} = 5$