On R, define aRb if and only if a−b is rational. What is the equivalence class of √2?
Answer and explanation
Correct answer: [√2] = {√2 + q : q ∈ Q}
The class of √2 contains exactly those real numbers x for which x−√2 is rational. Therefore x can be written as √2+q, where q belongs to Q, giving the set in option A. Option B is only the rational set, option C omits other valid numbers such as √2+1, and option D includes numbers whose difference from √2 may be irrational.
Frequently asked questions
What is the correct answer to this question?
[√2] = {√2 + q : q ∈ Q}
Why is this the correct answer?
The class of √2 contains exactly those real numbers x for which x−√2 is rational. Therefore x can be written as √2+q, where q belongs to Q, giving the set in option A. Option B is only the rational set, option C omits other valid numbers such as √2+1, and option D includes numbers whose difference from √2 may be irrational.
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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