Enter an example of an equivalence relation R on the set X = {0, 1, 2, 4, 8) such that all of the following are true: • (1, 4) = R; . (8,4) R; |[0] R = 3. ●
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![Enter an example of an equivalence relation R on the set X = {0, 1, 2, 4, 8} such that all of the following are true:
. (1, 4) = R;
• (8,4)
R;
• [0] R = 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3b40035-f597-40ed-a33a-d7bb8cece837%2F42674af1-9d4c-4d0b-bacc-99f0f4e0dd08%2Fxu71hsj_processed.jpeg&w=3840&q=75)
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- Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.a. 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 ].Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .