Let A = {1,2,3}, let S = P(A) and let RC S x S be a relation defined by the rule (X,Y) E R (XnY=0)^(XUY = A). (a) Prove or find a counterexample for the following properties: antisymmetry. • asymmetry. • symmetry. . irreflexivity/ • reflexivity. • transitivity • uniqueness

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