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Cosets of Subgroups of a Group

Modern Algebra
Group Theory (XXVII)
Subgroups of a Group
Cosets of Subgroups of a Group

For a subgroup H of G define a left coset of H in G as the set of all elements of the form ah, h in H.
Show that there is a 1-1 correspondence between the set of left cosets of H in G and the set of right cosets of H in G.

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It shows that there is a 1-1 correspondence between the set of left cosets of H in G and the set of right cosets of H in G.
The solution is detailed and well presented.

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