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If the set $\{a,b,c,d,e,f,g\}$ is is partitioned into these three partitions:

$\{a, c, e, g\}$

$\{b, d\}$

$\{f\}$

and an equivalence relation is produced by these partitions, is $\{a,c,e,g\}$ an equivalence class?

Josh1billion
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    That's not a partition: b is in two sets, and c is in none. – Chris Eagle Dec 07 '11 at 00:37
  • The relation you have defined ("$a~b$ iff $a$ and $b$ are both in the same set) not transitive: $a~b$ and $b~d$ but $a$ is not related to $d$. – Neal Dec 07 '11 at 00:41
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    Crap. I meant for the first one to say {a, c, e, g} instead of {a, b, e, g}. Fixed it now; thanks for pointing it out. – Josh1billion Dec 07 '11 at 00:53

1 Answers1

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As updated, yes. Wikipedia has more

Henry
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