Which of the following is not correct for relation R on the set of real numbers ?
Select the correct option:
A
$(x, y) \in R \Leftrightarrow 0<|\mathrm{x}|-|\mathrm{y}| \leq 1$ is neither transitive nor symmetric.
B
$(x, y) \in R \Leftrightarrow 0<|\mathrm{x}-\mathrm{y}| \leq 1$ is symmetric and transitive.
C
$(x, y) \in R \Leftrightarrow|x|-|\mathrm{y}| \leq 1$ is reflexive but not symmetric.
D
$(x, y) \in R \Leftrightarrow|x-y| \leq 1$ is reflexive and symmetric.
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Note that (1, 2) and (2, 3) satisfy 0 < |x − y| ≤ 1 but (1, 3) does not satisfy it, so 0 < |x − y| ≤ 1 is symmetric but not transitive, so (2) is correct.
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