Question

Let S be the set of all real numbers. Then the relation

R = {(a, b) : 1 + ab > 0} 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 (5) None of the above is true

Answer 1

Answer: (A)

Reflexive and symmetric but not transitive

Answer 2

Since $( a , a ) \in R$

∴ R is reflexive.

Also$1 + a b > 0$ ⇒ $1 + b a > 0$ ⇒$( b , a ) \in R$,

∴ R is symmetric.

$\because ( a , b ) \in R$ and $( b , c ) \in R$ need not imply $( a , c ) \in R$. Hence, R is not transitive.