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Mathematics
Which of the following is not correct for relation R on the set of real numbers ?
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Q. Which of the following is not correct for relation $R$ on the set of real numbers ?
JEE Main
JEE Main 2021
Relations and Functions - Part 2
A
$( x , y ) \in R \Leftrightarrow 0<| x |-| y | \leq 1$ is neither transitive nor symmetric.
B
$( x , y ) \in R \Leftrightarrow 0<| x - y | \leq 1$ is symmetric and transitive.
C
$( x , y ) \in R \Leftrightarrow| x |-| y | \leq 1$ is reflexive but not symmetric.
D
$( x , y ) \in R \Leftrightarrow| x - y | \leq 1$ is reflexive and symmetric.
Solution:
Correct answer is (b) $( x , y ) \in R \Leftrightarrow 0<| x - y | \leq 1$ is symmetric and transitive.