Most Important Selected Qs for JEE AdvancedMathematicsSets and Relations
On R , the set of real numbers, a relation is defined as a b if and only if 1+a b>0 . Then,
Options
- Ais an equivalence relation
- Bis reflexive and transitive but not symmetric
- Cis reflexive and symmetric but not transitive
- Dis only symmetric
Correct answer
C. is reflexive and symmetric but not transitive
Step-by-step solution
We know that, 1+a²>0, a R (a, a) is reflexive Again, let (a, b) 1+a b>0 1+b a>0 (b, a) is symmetric Now, (1,-0 1) and (-0 1,-9) but (1,-9) is not transitive.