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Question

On R, the set of real numbers, a relation ρ is defined as 'aρb if and only if 1+ab>0'. Then


Your Answer
A
ρ is an equivalence relation
Your Answer
B
ρ is reflexive and transitive but not symmetric 
Correct Answer
C
ρ is reflexive and symmetric but not transitive
Your Answer
D
ρ is only symmetric 

Solution

The correct option is C ρ is reflexive and symmetric but not transitive
For every aR,
1+a2>0
ρ is reflexive.

Let (a,b)ρ
1+ab>0
1+ba>0
(b,a)ρ
ρ is symmetric.

Let a=1,b=12,c=1
Then 1+ab>0 and 1+bc>0
But 1+ac0
Hence, ρ is not transitive.
 

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