1. Let R and S be relations on a set A. For each statement, conclude whether it is true or false. In each case, provide a proof or a counterexample, whichever applies.
(a) If R and S are transitive, then R υ S is also a transitive relation on A.
(b) If R is symmetric and transitive, then R is also reflexive.
(c) If R and S are partial orders on A, then R ∩ S is also a partial order on A.