A) reflexive
B) symmetric
C) transitive
D) None of these
Correct Answer: D
Solution :
Let \[A=\{1,2,3,4,5,6\}\] A relation R is defined on set A is \[R=\{(a,b):b=a+1\},\]therefore \[R=\{(1,2),(2,3),(3,4),(4,5)(5,6)\}\] Now, \[6\in A\]but (\[(6,6)\in /R\] Therefore, R is not reflexive. It can be observed that \[(1,2)\in R\]but (1, 2) \[(1,2)\in /R.\]Therefore, R is not symmetric. Now, \[(1,2),(2,3)\in R\]but \[(1,3)\in /R.\]Therefore, R is not transitive. Hence, R is neither reflexive nor symmetric nor transitive.
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