Recently I had one of my friends say to me that she heard from someone else, who she wont state the name, that I said I dont like her and now shes upset with me and believes them. Although I am 110% sure I never said a thing like that, even about anyone and I'm not sure what to do in positions like this. I told her I didn't but she doesn't believe me, so what am I supposed to do now to try and be the best Muslim in this situation?

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You've told her and she doesn't believe you. She has free will in what she thinks and no one can change that. There is no specific responsibility because she is not family where sile rahm becomes wajib. Make sure you don't do any wrong doing towards her