Which of the following is a subgroup of the g | vedclass

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(D) subset $H$ of a group $G$ is a subgroup if it is itself a group under the same operation.For $H = \{4^{n} \mid n \in \mathbb{Z}\}$,we note that $4

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$\{4^{n} \mid n \in \mathbb{Z}\}$

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(D) subset $H$ of a group $G$ is a subgroup if it is itself a group under the same operation.For $H = \{4^{n} \mid n \in \mathbb{Z}\}$,we note that $4^{n} = (2^{2})^{n} = 2^{2n}$. Since $2n \in \mathbb{Z}$ for all $n \in \mathbb{Z}$,$H \subset G$.$1.$ Closure: $4^{n} \cdot 4^{m} = 4^{n+m} \in H$.$2.$ Identity: $4^{0} = 1 = 2^{0} \in H$.$3.$ Inverse: For $4^{n} \in H$,the inverse is $4^{-n} \in H$.Thus,$\{4^{n} \mid n \in \mathbb{Z}\}$ is a subgroup of $G$.

Which of the following is a subgroup of the group $G = \{2^{n} \mid n \in \mathbb{Z}\}$ under multiplication?

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