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Dear Friends, ForumIAS Annual Community Meet will be held on June 25th at 11AM in Old Rajinder Nagar, New Delhi. The Chief Guest for the event will be Suharsh Bhagat, IAS Rank 5, CSE 2014. Come join us , and meet ForumIAS members who have secured ranks this year. Click here to register

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.


  • 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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