Let + be the set of positive integers. Let R be a binary relation on + + defined by (w,x)R(y,z) if

Let ℤ⁺ be the set of positive integers. Let R be a binary relation on ℤ⁺ × ℤ⁺ defined by (w,x)R(y,z) if and only if w divides y and x ≡ z (mod 2).
Is R reflexive? Is R symmetric? Is R antisymmetric? Is R transitive? [FULLY JUSTIFY EACH ANSWER]