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

3. Let X = {1, 2, 3, 4}. Let F be the set of all functions from X to X. For any relation R on X, define a relation S on F by: for all f, g ∈ F, f S g if and only if there exists x ∈ X so that f(x)Rg(x).

For each of the following statements, prove or disprove the statement.

(a) For all relations R on X, if R is reflexive then S is reflexive.

(b) For all relations R on X, if S is reflexive then R is reflexive.

(c) For all relations R on X, if R is symmetric then S is symmetric.

(d) For all relations R on X, if S is symmetric then R is symmetric.

Expert Solution

Colby Messinger answered 1 year ago

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