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.You need to login to perform this action.
You will be redirected in
3 sec