Is $\{a,c,e,g\}$ an equivalence class?

Question

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?

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 7, 2011 at 0:41
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 7, 2011 at 0:53

Henry · Accepted Answer · 2011-12-07 00:57:43Z

2

As updated, yes. Wikipedia has more

answered Dec 7, 2011 at 0:57

Henry

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$\begingroup$ Perfect, just what I needed to know. Thanks. $\endgroup$
– Josh1billion
Dec 7, 2011 at 0:59

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