A) Equivalence
B) Reflexive only
C) Reflexive and symmetric but not transitive
D) Reflexive and transitive but not symmetric
Correct Answer: A
Solution :
\[B=\left\{ {{b}_{1}},\,{{b}_{2}},\,{{b}_{3}} \right\},\,G=\left\{ {{g}_{1}},\,{{g}_{2}} \right\}\] \[\left( a,\,\,a \right)\in \,R\Rightarrow R\] is reflexive \[\left( a,\,b \right)\in R\Rightarrow \left( b,\,c \right)\in R\]; both a and b have same sex \[\Rightarrow R\] is symmetric Also \[\left( a,\,\,b \right)\in \,R\Rightarrow \left( b,\,\,c \right)\,\in R\Rightarrow \left( a,\,\,c \right)\in R\] \[\Rightarrow R\]is transitive.
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