(a) Prove that a nonempty subset H of a group G is a subgroup if and...

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(a) Prove that a nonempty subset H of a group G is a subgroup if and only if ab 1e H whenever a, b e H. [6] (b) Find the order of an element (1 3 2) in Sg. [5] (c) Show that every subgroup of index 2 is normal. [5] (d) Find the index of (2) in Z. [4] (a) Prove that a nonempty subset H of a group G is a subgroup if and only if ab 1e H whenever a, b e H. [6] (b) Find the order of an element (1 3 2) in Sg. [5] (c) Show that every subgroup of index 2 is normal. [5] (d) Find the index of (2) in Z. [4]