Let S be the set of all real numbers. Then, the relation R = { a , b : 1 + a b 0 } on S is

Question

Let S be the set of all real numbers. Then, the relation R = { a , b : 1 + a b > 0 } on S is, reflexive and symmetric but not transitive, reflexive and transitive but not symmetric, reflexive, transitive and symmetric, None of the above

MARKS App · Accepted Answer

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.

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