Because 'span of' is an operation on sets we naturally consider how it interacts with the usual

Question:

Because 'span of' is an operation on sets we naturally consider how it interacts with the usual set operations.
(a) If S ⊂ T are subsets of a vector space, is [S] ⊂ [T]? Always? Sometimes? Never?
(b) If S, T are subsets of a vector space, is [S ∪ T] = [S] ∪ [T]?
(c) If S, T are subsets of a vector space, is [S ∩ T] = [S] ∩ [T]?
(d) Is the span of the complement equal to the complement of the span?