For each of the following relations on the set specified, determine whether the relation is reflexive, symmetric, antisymmetric, or transitive. Also determine whether it is a partial order or an equivalence relation, and, if the latter, describe the partition induced by the relation.
(a) R is the relation on Q where aRb if |a - b| < 1.
(b) Let T be the set of all triangles in the plane. For t1, t2 ∈ T, define t1 R t2 if t1, t2 have the same area.
(c) For T as in part (b), define R by t1 R t2 if at least two sides of t1 are contained within the perimeter of t2.
(d) Let A = {1, 2, 3, 4, 5, 6, 7}. Define R on A by x R y if xy ≥ 10.