3. Let X = {1, 2, 3, 4}. Let F be the set of all functions fromX to X. For any relation R on X, define a relation S on F by: forall f, g ∈ F, f S g if and only if there exists x ∈ X so thatf(x)Rg(x).
For each of the following statements, prove or disprove thestatement.
(a) For all relations R on X, if R is reflexive then S isreflexive.
(b) For all relations R on X, if S is reflexive then R isreflexive.
(c) For all relations R on X, if R is symmetric then S issymmetric.
(d) For all relations R on X, if S is symmetric then R issymmetric.
