Determine whether the following binary relations are reflexive, symmetric, antisymmetric and transitive:

a . x R y ⇔ x y ≥ 0∀ x, y ∈ R

b . x R y ⇔ x > y ∀ x, y ∈ R

c . x R y ⇔ |x|= |y| ∀ x, y ∈ 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 classe