Equivalence Relation on a Group Two Proofs

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Equivalence Relation on a Group Two Proofs. Given a group G and a subgroup H of G, we prove that the relation x=y if xy^{-1} is in H is an equivalence relation on G. Then cosets are defined and we prove that s_1 = s_2 iff [s_1] = [s_2].

[@MrCoreyTexas]

one thing about cosets is, they are not necessarily subgroups of the group G- but exactlty one of them is, the one with the identity element

[@TheMathSorcerer]

[@JawadAli-tj3ec]

Helpful

[@TheMathSorcerer]

awesome very happy it helped!!