Verified Solution • 2025–26 Session moderate

QJEEM21Mad29c: JEE Main 2021 Mathematics - Class 11 JEEM21Mad29c Solution: Which of the following is not correct for relation R on the set …

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

Multiple Choice Options

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

Step-by-Step Verified Solution

Note that (a, b) and (b, c) satisfy 0 < |x

-

\le

1 but (a, c) does not satisfy it so 0

\le

-

\le

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.

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