A) reflexive
B) symmetric
C) transitive
D) None of these
Correct Answer: B
Solution :
Idea A relation R on set A is said to be symmetric if\[(a,b)\in R\Rightarrow (b,a)\in R,\forall a,b\in A\] Since, it is given that \[R\cap R'\]is not disjoint. \[\therefore \]There is atleast one ordered pair, say, (a, b) in \[\Rightarrow \]\[(a,b)\in R\]and\[(a,b)\in R'\] Since, it is also given that R and R' are symmetric relations, we get\[(b,a)\in R'\]and\[(b,a)\in R'\]\[\Rightarrow \]\[(b,a)\in R\cap R'\] \[\Rightarrow R\cap R'\]is symmetric. TEST Edge Identify relation, reflexive relation, symmetric relation related questions are asked. To solve these types of questions to understand the basic definition of these relations.
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