Medium MCQ +4 / -1 PYQ · JEE Mains 2021

Which of the following is not correct for relation R on the set of real numbers ?

  1. A (x, y) $\in$ R $\Leftrightarrow$ 0 < |x| $-$ |y| $\le$ 1 is neither transitive nor symmetric.
  2. B (x, y) $\in$ R $\Leftrightarrow$ 0 < |x $-$ y| $\le$ 1 is symmetric and transitive. Correct answer
  3. C (x, y) $\in$ R $\Leftrightarrow$ |x| $-$ |y| $\le$ 1 is reflexive but not symmetric.
  4. D (x, y) $\in$ R $\Leftrightarrow$ |x $-$ y| $\le$ 1 is reflexive nd symmetric.

Solution

Note that (a, b) and (b, c) satisfy 0 &lt; |x $-$ y| $\le$ 1 but (a, c) does not satisfy it so 0 $\le$ |x $-$ y| $\le$ 1 is symmetric but not transitive. <br><br>For example, <br><br>x = 0.2, y = 0.9, z = 1.5 <br><br>0 ≤ |x – y| = 0.7 ≤ 1 <br><br>0 ≤ |y – z| = 0.6 ≤ 1 <br><br>But |x – z| = 1.3 &gt; 1 <br><br>So, (b) is correct.

About this question

Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations

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