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I study group theory on my own, and saw an exercise:

Prove or disprove: If $G$ is a group, and $H\leq G, K\leq G$, Every coset of $H \cap K$ is an intersection of cosets of $H$ and $K$.

I saw similar questions here but they all take into account if these are left or right cosets, and the empty set so I thought that I should disprove it maybe with a left coset and a right coset, but can't come up with ideas.

Can you give me a hint?

Thanks :)

Yo Lo
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    The duplicate assumes left cosets, but it doesn't matter. If you prefer you can think also of right cosets. Of course "coset" here means only one sort of coset. Do you agree that the duplicate solves your question? – Dietrich Burde Apr 04 '22 at 09:13
  • The thing I'm not so sure about is why it doesn't matter and why it only means one sort of coset..Is it just because an intersection of a left and right coset is the empty set? – Yo Lo Apr 04 '22 at 09:44
  • By Definition the word coset means "left coset" (or "right coset", but no mixture except if the group is abelian, where right is left). So the question really is:"Prove or disprove:... Every left coset is..." – Dietrich Burde Apr 04 '22 at 11:51

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