Let R be an equivalence relation on A and let [a] and [b] denote equivalence classes. If aRb, which statement must be true?
Answer and explanation
Correct answer: [a]=[b]
For an equivalence relation, related elements belong to the same equivalence class. If aRb, then every element related to a is also related to b, using symmetry and transitivity, and the reverse inclusion follows similarly. Hence [a]=[b]. Distinct equivalence classes are disjoint, but these two are not distinct. Options C and D contradict the possibility of other elements being equivalent to a or b.
Frequently asked questions
What is the correct answer to this question?
[a]=[b]
Why is this the correct answer?
For an equivalence relation, related elements belong to the same equivalence class. If aRb, then every element related to a is also related to b, using symmetry and transitivity, and the reverse inclusion follows similarly. Hence [a]=[b]. Distinct equivalence classes are disjoint, but these two are not distinct. Options C and D contradict the possibility of other elements being equivalent to a or b.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
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