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  4. The maximum number of equivalence relations can be defined on the set A= 1,2,3 are

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

Solution:

$R_{1}=\{(1,1),(2,2),(3,3)\}$
$R_{2}=\{(1,1),(2,2),(3,3),(1,2),(2,1)\}$
$R_{3}=\{(1,1),(2,2),(3,3),(1,3),(3,1)\}$
$R_{4}=\{(1,1),(2,2),(3,3),(2,3),(3,2)\}$
$R_{5}=\{(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)\}$