For the relation R1 defined on R by the rule (a,b)ϵR1⇔1+ab>0. Prove

1.	For the relation R1 defined on R by the rule (a,b)ϵR1⇔1+ab>0. Prove that : (a,b)ϵR1 and (b,c)ϵR1 ⇒(a,c)ϵR1 is not true for all a,bcϵR
Answer» For the relation $R_{1}$ defined on R by the rule $(a, b) ϵ R_{1} \Leftrightarrow 1 + a b > 0.$ Prove that : $(a, b) ϵ R_{1}$ and $(b, c) ϵ R_{1}$ $\Rightarrow (a, c) ϵ R_{1}$ is not true for all $a, b c ϵ R$

For the relation R1 defined on R by the rule (a,b)ϵR1⇔1+ab>0. Prove that : (a,b)ϵR1 and (b,c)ϵR1 ⇒(a,c)ϵR1 is not true for all a,bcϵR

Answer»

For the relation $R_{1}$ defined on R by the rule $(a, b) ϵ R_{1} \Leftrightarrow 1 + a b > 0.$

Prove that : $(a, b) ϵ R_{1}$ and $(b, c) ϵ R_{1}$

$\Rightarrow (a, c) ϵ R_{1}$ is not true for all $a, b c ϵ R$