The following statements are made about (right) cosets of a subgroup H of a group G. Say whether each statement is true or false and give a reason for your answer. (i) H itself is a coset. (ii) Every element of G belongs to a coset. (iii) If y is in a coset Hx, then Hy = Hx. (iv) Two cosets Hx and Hy are either the same, or they are disjoint, HxHy = 0. 1 (v) Hx = Hy if and only if xy-¹ € H.

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