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Let X be the set {1, 2, 3}. a)For each function f in the set of...

Let X be the set {1, 2, 3}.

a)For each function f in the set of functions from X to X, consider the relation that is the symmetric closure of the function f'. Let us call the set of these symmetric closures Y. List at least two elements of Y.

b) Suppose R is some partial order on X. What is the smallest possible cardinality R could have? What is the largest?

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