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total number of eqvivalence relation defined in the set S={a,b,c} is

total number of eqvivalence relation defined in the set S={a,b,c} is

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1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Since there is a one-to-one correspondence between partitions of sets
and equivalence relations, it suffices to count the number of partitions
of a set with three elements. Let S = {a, b, c}. Then the possible
partitions are:
{S}=
{{a}, {b, c}},
{{b}, {a, c}},
{{c}, {a, b}},
{{a}, {b}, {c}}.
In particular, there are five different partitions on S and hence five
different equivalence relations which can be imposed on S.
Thanks and Regards
Shaik Aasif
askIITians faculty

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