can anyone solve this question from modern algebra?

S is a subset of a given group G and one defines a relation a~b in G if and only if ab^-1 belongs to S .Show that the necessary and sufficient condition that this is an equivalence relation is that S is a subgroup of G.

Comments

  • is there anyone to prove it......plzz help karo....
  • First assume that ~ is an equivalence relation and then prove that S is a subgroup.
    Then suppose S to be subgroup and prove that ~ is an equivalence relation.
    In which part you are facing problem?
  • BC maths Philosophy se zyada other worldly lagta hai!!
    pre - 2, mains - 1*
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