Determine whether the relation r on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ r if and only if:

(a) x + y = 0, (b) x = ±y, (c) x − y is a rational number, (d) x = 2y, (e) xy ≥ 0, (f) xy = 0, (g) x = 1, (h) x = 1 or y = 1.