Let R be an equivalence relation on A and let [a] and [b] denote equivalence classes. If aRb, which statement must be true?

Correct answer: [a]=[b]

Correct answer: A. The equivalence class [a] is the set of all elements x in A such that xRa. If aRb, symmetry gives bRa. To show [a] is contained in [b], take any x in [a], so xRa. Since aRb, transitivity gives xRb, which means x belongs to [b]. The reverse inclusion is obtained similarly: if xRb, then bRa by symmetry, and transitivity gives xRa, so x belongs to [a]. Thus [a]=[b]. Option B is false because distinct equivalence classes are disjoint, but aRb means these two classes are the same class, not distinct. Option C is false because an equivalence class may contain many elements; it contains only a only in a special relation, not in general. Option D is the opposite of what equivalence means: b itself is related to a, and every member of the common class is related to a. Memory cue: in an equivalence relation, related elements are simply different representatives of the same class.