For the relation R 1 defined on R by the rule a - b - R 1- 1- ab -0Prove that - a - b - R 1 and b - c - R 1- a - c - R 1 is not true for all a- bc - R

Let (1, 1/2) ϵ R_1 and ( 1/2, 4) ϵ R_1 ⇒ 1 + 1 × 1/2 gt; 0 and 1 + ( 1/2) 4 gt; 0 But, 1 + 1 × ( 4) = 1 4 = 3 lt; 0 So, (1, 4) ϵ̸ R_1 ...

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Definition of Relations

For the relat...

Question

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 $a, b c ϵ R$

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