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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Sets and Relations

JEE Main · Mathematics · Sets and Relations

Let S be the set of all real numbers. Then, the relation R = (a,...

Let SS be the set of all real numbers. Then, the relation R=(a,b):1+ab>0R = { \left(a, b\right): 1 + ab > 0 } on SS is

Options

  1. Areflexive and symmetric but not transitive
  2. Breflexive and transitive but not symmetric
  3. Creflexive, transitive and symmetric
  4. DNone of the above

Correct answer

A. reflexive and symmetric but not transitive

Step-by-step solution

R=(a,b):1+ab>0R = { \left(a, b\right): 1 + ab > 0 }
(i) (1,1)∈R( 1, 1 ) \in R

(ii) (1,2)∈R⇒(2,1)∈R( 1, 2 ) \in \mathbb{R} ⇒ ( 2, 1 ) \in R

(iii) (1,2)∈Rand(2,3)∈R⇒(1,3)∈R( 1, 2 ) \in Rand ( 2, 3 ) \in \mathbb{R} ⇒ ( 1, 3 ) \in R
It is clear that the given relation on SS is reflexive, symmetric but not transitive.

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