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- Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.29. Suppose , , represents a partition of the nonempty set A. Define R on A by if and only if there is a subset such that . Prove that R is an equivalence relation on A and that the equivalence classes of R are the subsets .Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .
- Label each of the following statements as either true or false. Every upper bound of a nonempty set is a least upper bound.8. a. Prove that the set of all onto mappings from to is closed under composition of mappings. b. Prove that the set of all one-to-one mappings from to is closed under composition of mappings.Label each of the following statements as either true or false. If a nonempty set contains an upper bound, then a least upper bound must exist in .