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Question

Let R be a relation defined in the set of real numbers by a R b1+ab>0. Then R is

A
Equivalence relation
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B
Transitive
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C
Symmetric
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D
Anti-symmetric
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Solution

The correct option is C Symmetric
i) Reflexive: Let R' be the set of real numbers
Let aR1+a.a=1+a2>0
(a,a)R i.e R is reflexive
ii) Symmetric: a,bR
Let (a,b)R1+a.b>01+b.a>0(b,a)R
i.e R is symmetric
iii) Transitive: The relation R is not transitive because we find that (2,12)R and (12,2)R
but (2,2)R
since 1+2(2)=3 which is not positive
Hence R is reflexive, symmetric but not transitive

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