A) Reflexive and symmetric but not transitive
B) Reflexive and transitive but not symmetric
C) Symmetric, transitive but not reflexive
D) Reflexive, transitive and symmetric
E) None of the above is true
Correct Answer: A
Solution :
Since\[1+a.a=1+{{a}^{2}}>0\,,\forall a\in S\], \ \[(a,\,a)\in R\] \ R is reflexive. Also\[(a,b)\in R\] Þ \[1+ab>0\] Þ \[1+ba>0\] Þ\[(b,\,a)\in R\], \ R is symmetric. \[\because (a,\,b)\in R\] and\[(b,\,c)\in R\] need not imply \[(a,\,c)\in R\]. Hence, R is not transitive.
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