On R, the set of real numbers, a relation ρ is defined as 'aρb if and only if 1+ab>0'. Then
ρ is an equivalence relation
ρ is reflexive and transitive but not symmetric
ρ is reflexive and symmetric but not transitive
The correct option is C ρ is reflexive and symmetric but not transitive
For every a∈R,
∴ρ is reflexive.
∴ρ is symmetric.
Then 1+ab>0 and 1+bc>0
Hence, ρ is not transitive.