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 equivalenve class without using the results of Lemma 8.3.2, Lemma 8.3.3, or Theorem 8.3.4.
For every a,b, and c in A, if b R c and then
For all a, b and c in A, if b R c and c ∈ [ a ] then b ∈ [ a ].
Let R be an equivalence relation on a set A.
R is an equivalence relation on a set A.
By the definition of
Since R is an equivalence relation, R is reflexive, symmetric and transitive
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