Let ~ denote an equivalence relation on a set A. Prove that
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- Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.arrow_forwarda. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the equivalence class [ 3 ]. b. Let R be the equivalence relation congruence modulo 4 that is defined on Z in Example 4. For this R, list five members of equivalence class [ 7 ].arrow_forwardProve Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .arrow_forward
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