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1.Relation and Function
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Which of the following is not correct for relation $\mathrm{R}$ on the set of real numbers ?
A
$(\mathrm{x}, \mathrm{y}) \in \mathrm{R} \Leftrightarrow 0<|\mathrm{x}|-|\mathrm{y}| \leq 1$ 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
$(\mathrm{x}, \mathrm{y}) \in \mathrm{R} \Leftrightarrow|\mathrm{x}-\mathrm{y}| \leq 1$ is reflexive and symmetric.
(JEE MAIN-2021)
Solution
Note that $(1,2)$ and $(2,3)$ satisfy $0<|x-y| \leq 1$
but $(1,3)$ does not satisfy it so
$0 \leq|\mathrm{x}-\mathrm{y}| \leq 1$ is symmetric but not transitive
Standard 12
Mathematics
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