Let R be an equivalence relation on a set A. Prove the following statement directly from the definitions of equivalence relation and equivalence class. For every a and b in A, if [a] = [b] then a Rb. Some of the sentences in the following scrambled list can be used to prove the statement. By definition of equivalence class, a E[b]. Let b E[a]. Then by definition of equivalence class, b Ra. Since R is symmetric, if b R a then a R b. | Thus, a Ra, and so, by definition of equivalence class, a E [a]. Since [a] = [b] and a E [a], then a E [b] by definition of set equality. | Hence, by definition of equivalence class, a Rb. By definition of equivalence relation, R is reflexive. Proof: Construct a proof by selecting appropriate sentences from the list and putting them in the correct order. 1. Suppose R is an equivalence relation on a set A, a and b are in A, and [a] = [b]. 2. —Select— 3. —-Select— 4. —Select— 5. —Select—