Let R be an equivalence relation on a set A. Prove each of the statements in 36-41 directly from the definitions of equivalence relation and equivalence class without using the results of the Lemma 8.3.2, Lemma 8.3.3, or Theorem 8.3.4.
For every a and b in A, if
For all a and b in A, if b ∈ [ a ] then a R b.
Let R be an equivalence relation on a set A.
R is an equivalence relation on a set A
By the definition of
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