A) reflexive and symmetric
B) symmetric only
C) transitive only
D) anti-symmetric only
Correct Answer: A
Solution :
\[|a-a|=0<1\]\[\therefore \]\[aRa\forall a\in R\] \[\therefore \]R is not anti-symmetric Again, \[aRb\Rightarrow \left| a-b \right|\le \,1\Rightarrow |b-a|\le 1\Rightarrow bRa\] \[\therefore \] R is symmetric, again \[|R\frac{1}{2}and\frac{1}{2}R|\] but \[\frac{1}{2}\ne 1\] Further,\[1R2\] and 2R 3 but1 r 3 \[[\because |1-3|=2>1]\] \[\therefore \] R is not transitive.
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