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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

  1. Ais an equivalence relation
  2. Bis reflexive and transitive but not symmetric
  3. Cis reflexive and symmetric but not transitive
  4. 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.

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