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We know that aH = bH iff a is in bH or b is in aH. Does this mean that any element of a coset can be its representative? I.e. can 'b' be called as the coset representative of aH, if b is also in aH?

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    $\begingroup$ Yes that's right $\endgroup$
    – Derek Holt
    Jul 13, 2021 at 11:38
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    $\begingroup$ Sure, it can. Every element of the equivalence class of an equivalence relation is a representative of that class. $\endgroup$
    – MphLee
    Jul 13, 2021 at 11:39
  • $\begingroup$ Thanks! Made the idea of cosets much clear! $\endgroup$
    – Sasikuttan
    Jul 13, 2021 at 11:43
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    $\begingroup$ I believe that of your is more a terminological doubt. I suggest you to brush the concept of equivalence relation and partition in equivalence classes. $\endgroup$
    – MphLee
    Jul 13, 2021 at 11:45

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