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Definition 2.3.2 in our book defines the power set of a set S, denoted by P(S),...

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Advance Math

Definition 2.3.2 in our book defines the power set of a set S,denoted by P(S), as the set of all subsets of S, that is P(S) = {A: A ? S}. For example, P({1, 2}) = {?, {1}, {2}, {1, 2}}, and P(?)= {?}. Consider the relation ? on the power set P(Z), i.e. theis-a-subset-of relation defined on sets of integers. In otherwords, the objects we compare are sets of integers. (a) Prove ordisprove: ? is reflexive. (b) Prove or disprove: ? is irreflexive.(c) Prove or disprove: ? is symmetric. (d) Prove or disprove: ? isantisymmetric. (e) Prove or disprove: ? is transitive. (f) Is ? onZ an equivalence relation? Is it a partial order? (g) Which otherrelation satisfies exactly the same properties?

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