Equivalence Relations Week 5 Prove this statement from the definition of an equivalence relation: Let A be a nonempty set and let R be an equivalence relation on the set A . Then, a A, a [a]. a,b A, a R b [a]=[b] For each a,b A, [a]=[b] [a][b] = Also prove the collection C of all equivalence classes determined by R is a partition of the set A.