Published by:
CGP EDU Academic Team
Published on: August 11, 2026
Which of the following is not correct for relation R on the set of real numbers?
A
(x, y) 
R 
0 < |x| − |y| ≤ 1 is neither transitive nor symmetric.
R 0 < |x| − |y| ≤ 1 is neither transitive nor symmetric.
B
(x, y) 
R 
0 < |x − y| ≤ 1 is symmetric and transitive.
R 0 < |x − y| ≤ 1 is symmetric and transitive.
C
(x, y) 
R 
|x| − |y| ≤ 1 is reflexive but not symmetric.
R |x| − |y| ≤ 1 is reflexive but not symmetric.
D
(x, y) 
R 
|x − y| ≤ 1 is reflexive and symmetric.
R |x − y| ≤ 1 is reflexive and symmetric.
Text Solution
Verified by ExpertsThe correct answer is:
B
Note that (1, 2) and (2, 3) satisfy 0 < |x − y| ≤ 1
but (1, 3) does not satisfy it so
0 ≤ |x − y| ≤ 1is symmetric but not transitive
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