Question: Subspaces are subsets and so we naturally consider how 'is a subspace of' interacts with the usual set operations. (a) If A, B are subspaces

Subspaces are subsets and so we naturally consider how 'is a subspace of' interacts with the usual set operations.
(a) If A, B are subspaces of a vector space, must their intersection A ∩ B be a subspace? Always? Sometimes? Never?
(b) Must the union A ∪ B be a subspace?
(c) If A is a subspace, must its complement be a subspace?

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