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 Lemma 8.3.2, Lemma 8.3.3, or Theorem 8,3,4.
For every a in
For all a in A, a ∈ [ a].
Let R be an equivalence relation on a set A.
R is an equivalence relation on a set A.
Since R is an equivalence relation, R is reflexive, symmetric and transitive.
By the definition of reflexive:
or equivalently a R a
By the definition of :
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