Let be the vector space of all sequences. Denote by the set of all arithmetic sequences and by the set of all geometric sequences. Then

Question

Let    be the vector space of all sequences. Denote by    the set of all arithmetic sequences and by    the set of all geometric sequences. Then

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is a vector subspace of    but    is not.

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Neither    nor    are vector subspaces of  .

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is a vector subspace of    but    is not.

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Both    and    are vector subspaces of   .

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