JEE Mains · Maths · STD 12 - 1. relation and function
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.
Answer & Solution
Correct Answer
(B) \((x, y) \in R \Leftrightarrow 0<|x-y| \leq 1\) is symmetric and transitive.
Step-by-step Solution
Detailed explanation
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
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