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NTA Abhyas JEE Main2020MathematicsSets and RelationsPractice

Consider a relation R defined as a R b if 2 + a b > 0 where a , b are real numbers. Then, the relation R is

Options

  1. Areflexive and symmetric
  2. Bsymmetric and transitive
  3. Ctransitive and reflexive
  4. DNone of these

Correct answer

A. reflexive and symmetric

Step-by-step solution

Relation R is reflexive, since 2 + a × a > 0 ,   ∀ real number a . It is symmetric, since 2 + a b > 0 ⇒ 2 + b a > 0 . However, R is not transitive. Consider three real numbers 2 , - 1 6 and - 2 . We have 2 + 2 × - 1 6 = 5 3 > 0 and 2 + - 1 6 - 2 = 7 3 > 0 So, 2 R - 1 6 and - 1 6 R - 2 But, 2 R - 2 since 2 + 2 - 2 = - 2 ≯ 0

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