99 Percentile Qs Bank for JEE MainMathematicsSets and Relations
Let S be the set of all real numbers. Then, the relation R = a , b : 1 + a b > 0 on S is
Options
- Areflexive and symmetric but not transitive
- Breflexive and transitive but not symmetric
- Creflexive, transitive and symmetric
- DNone of the above
Correct answer
A. reflexive and symmetric but not transitive
Step-by-step solution
R = a , b : 1 + a b > 0 (i) ( 1 , 1 ) ∈ R (ii) ( 1 , 2 ) ∈ R ⇒ ( 2 , 1 ) ∈ R (iii) ( 1 , 2 ) ∈ R and ( 2 , 3 ) ∈ R ⇒ ( 1 , 3 ) ∈ R It is clear that the given relation on S is reflexive, symmetric but not transitive.