Find the maximum number of equivalence relations on the set A={1,2,3} .
Find the maximum number of equivalence relations on the set A={1,2,3} :
There is a maximum of 5 equivalence relations on the set A={1,2,3}
They are
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)}
Hence,the Maximum number of equivalence relation's is '5'