Let H and K be subgroups of a group G. Define ~ on G by a ~

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Let H and K be subgroups of a group G. Define ~ on G by a ~ b if and only if a = hbk for some h ∈ H and some k ∈ K. 

a. Prove that ~ is an equivalence relation on G. 

b. Describe the elements in the equivalence class containing a ∈ G. (These equivalence classes are called double cosets.)

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