1) Let the set $$ G $$ be defined by $$ G=\left\{\left.\begin{array}{l}k \ 2\end{array} \right\rvert\, k \in \mathbb{Z}\right\} \cup\{0\} $$ prove that $$ G $$ is a group under usual addition

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To prove that $$ G $$ is a group under addition, we need to show closure, associativity, the presence of an identity element (0), and the existence of inverse elements for all elements in $$ G $$. Since $$ G $$ consists of integers and the number 2, along with 0, it satisfies all group properties.

1) Let the set \( G \) be defined by \[ G=\left\{\left.\begin{array}{l}k \\ 2\end{array} \right\rvert\, k \in \mathbb{Z}\right\} \cup\{0\} \] prove that \( G \) is a group under usual addition

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1) Let the set \( G \) be defined by \[ G=\left\{\left.\begin{array}{l}k \\ 2\end{array} \right\rvert\, k \in \mathbb{Z}\right\} \cup\{0\} \] prove that \( G \) is a group under usual addition

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