Conversely, every partition on a set can be used to form an equivalence relation. Let I=A,A2.A be a partition of a nonempty set A. Let r be a relation on A, and arb if only if there exists A; Ell s.t. a,b∈A ie.R=(A1×A1)∪U(A2×A2)U….∪(An×An) R is an equivalence relation on A Theorem 2.12: Given a partition AiEZ of the set A, there is an equivalence relation R that has the set A s iEZ, as its equivalence classesConversely, every partition on a set can be used to form an equivalence relation. Let ={A1 ,A2 ,…,An } be a partition of a nonempty set A. Let R be a relation on A, and aRb if only if there exists Ai s.t. a,bAi . i.e. R=(A1A1 )∪(A2A2 )∪…∪(AnAn ) R is an equivalence relation on A Theorem 2.12：Given a partition {Ai |iZ} of the set A, there is an equivalence relation R that has the set Ai , iZ, as its equivalence classes