III. Consider the relation $R_4$ that is a partial order.
Answer:
(i) $R_4$ is reflexive, symmetric, antisymmetric, and transitive.
(ii) $R_4$ is reflexive, symmetric, antisymmetric, and NOT transitive.
(iii) $R_4$ is reflexive, NOT symmetric, antisymmetric, and transitive.
(iv) $R_4$ is reflexive, symmetric, NOT antisymmetric, and NOT transitive.
(v) $R_4$ is NOT reflexive, symmetric, antisymmetric, and transitive.