Let R be an equivalence relation on a set A. Prove each of the statements in 36-41 directly from the definitions of equivalence reation and equivalence class without using the results of Lemma 8.3.2, Lemma 8.3.3, or theorem 8.3.4.
For every a and b in A, if [a]=[b] then aRb.
For all a and b in A, if [ a ] = [ b ] then a R b.
Let R be an equivalence relation on a set A.
R is an equivalence relation on a set A.
In one of the previous exercises, we showed that (which followed from the reflexive property of R and the definition of
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