Determine whether the following binary relations are reflexive, symmetric, antisymmetric and transitive:
a. xRy ⇔ xy ≥ 0 ∀x, y in the set R
b. xRy ⇔ x > y ∀x, y in the set R
c. xRy ⇔ |x| = |y| ∀x, y in the set R
For each of the above, indicate whether it is an equivalence relation or a partial order. If it is a partial order, indicate whether it is a total order. If it is an equivalence relation, describe its equivalence classes.