3. Let A = {1, 2, 3}, let S = P(A) and let RC S x S be a relation defined by the rule (X,Y) ER⇒ (XnY=0)A (XUY = A). (a) Prove or find a counterexample for the following properties: • antisymmetry • asymmetry. symmetry. • irreflexivity/ • reflexivity. • transitivity • uniqueness (b) Based on the findings from the previous point, conclude whether R is a graph, partially ordered set, equivalence relation, or a function (several answers may hold simultaneously). Analyze the relation R.

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A: topic -  homogenous funtion