Question: Please provide the steps and Theorems used. Let M be an abelian group and D a subgroup. For any element m of M , where

Please provide the steps and Theorems used.

Let M be an abelian group and D a subgroup. For any element m of M , where m has order 2, define mD={md I d is an element of D} . Prove that the set C=D U mD is a subgroup of M .

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