A) Reflexive and Symmetric
B) Symmetric only
C) Transitive only
D) Anti-symmetric only
Correct Answer: A
Solution :
\[|a-a|=0<1\] \[\therefore \,a\,R\,a\,\forall \,a\in R\] \[\therefore \] R is reflexive. Again a R b Þ \[|a-b|\le 1\Rightarrow |b-a|\le 1\Rightarrow bRa\] \[\therefore \] R is symmetric, Again \[1R\frac{1}{2}\] and \[\frac{1}{2}R1\] but \[\frac{1}{2}\ne 1\] \[\therefore \] R is not anti-symmetric. Further, 1 R 2 and 2 R 3 but \[1\,\not{R}\,3\], [\[\because \,|1-3|=2>1\]] \[\therefore \] R is not transitive.
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