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Show that the σ-algebra B of Borel sets contains all closed sets.
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- Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.In Exercises , prove the statements concerning the relation on the set of all integers. 17. If and , then .