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

There are maximum 5 equivalence relations on the set A={1,2,3}. They are
<ul>
R1={(1,1),(2,2),(3,3)}
R2={(1,1),(2,2),(3,3),(1,2),(2,1)}
R3={(1,1),(2,2),(3,3),(1,3),(3,1)}
R4={(1,1),(2,2),(3,3),(2,3),(3,2)}
R5={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}
</ul>

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