Questions
Let S be the set of all real numbers. Then the relation on S is
a
Reflexive and symmetric but not transitive
b
Reflexive and transitive but not symmetric
c
Symmetric, transitive but not reflexive
d
Reflexive, transitive and symmetric
detailed solution
Correct option is A
Since 1+a.a=1+a2>0, ∀a∈S, ∴ (a, a)∈R∴ R is reflexive. Also a, b∈R⇒1+ab>0⇒1+ba>0⇒(b, a)∈R,∴R is symmetric.∵(a, b)∈R and (b, c)∈R need not imply (a, c)∈R.Hence, R is not transitive.Talk to our academic expert!
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