1
$\begingroup$

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?

  • 6
    That's not a partition: b is in two sets, and c is in none.2011-12-07
  • 0
    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 $d$.2011-12-07
  • 1
    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.2011-12-07

1 Answers 1

2

As updated, yes. Wikipedia has more

  • 0
    Perfect, just what I needed to know. Thanks.2011-12-07