Question: Let X be a linear space. Two affine subsets S and T are parallel if one is a translate of the other, that is, S

Let X be a linear space. Two affine subsets S and T are parallel if one is a translate of the other, that is,
S = T + x for some x ∈ X
Show that the relation S is parallel to T is an equivalence relation in the set of affine subsets of X.

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