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Let F = {A ⊆ Z : |A| < ∞} be the set of all finite...

Let F = {A ⊆ Z : |A| < ∞} be the set of all finite sets of integers. Let R be the relation on F defined by A R B if and only if |A| = |B|. (a) Prove or disprove: R is reflexive. (b) Prove or disprove: R is irreflexive. (c) Prove or disprove: R is symmetric. (d) Prove or disprove: R is antisymmetric. (e) Prove or disprove: R is transitive. (f) Is R an equivalence relation? Is it a partial order?

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