A) Symmetric and transitive but not reflexive
B) Universal relation
C) Equivalence relation
D) Reflexive but not symmetric and transitive.
Correct Answer: C
Solution :
Since \[\left( a,\,a \right)\in R\Rightarrow R\] is reflexive Also \[\left( a,\,b \right)\in R\Rightarrow \left( b,\,\,a \right)\in R\] Both voters can be interchanged \[\therefore \] R is symmetric Again \[\left( a,\,b \right)\in R,\,\left( b,\,\,c \right)\in R\Rightarrow \left( a,\,c \right)\in R\] \[\therefore \] R is transitive Hence 'R' is an equivalence relation.
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