JEE Main 2021 — Sets And Relations Question with Solution
From: JEE Main 2021 (Online) 31st August Morning Shift
Question
Which of the following is not correct for relation R on the set of real numbers ?
Choose an option
Show full solutionCorrect option: B
Correct answer
B(x, y) R 0 < |x y| 1 is symmetric and transitive.
Step-by-step explanation
Note that (a, b) and (b, c) satisfy 0 < |x y| 1 but (a, c) does not satisfy it so 0 |x y| 1 is symmetric but not transitive.
For example,
x = 0.2, y = 0.9, z = 1.5
0 ≤ |x – y| = 0.7 ≤ 1
0 ≤ |y – z| = 0.6 ≤ 1
But |x – z| = 1.3 > 1
So, (b) is correct.
For example,
x = 0.2, y = 0.9, z = 1.5
0 ≤ |x – y| = 0.7 ≤ 1
0 ≤ |y – z| = 0.6 ≤ 1
But |x – z| = 1.3 > 1
So, (b) is correct.
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This is a previous-year question from JEE Main 2021, covering the Sets And Relations chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.