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Question

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


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Solution

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'


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