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  3. 3. let x = {1, 2, 3, 4}. let f be the set of all..

3. Let X = {1, 2, 3, 4}. Let F be the set of all...

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Advance Math

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.

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