Answer 1

We have:
(a, b) ∈ R₁ ⇔ 1 + ab > 0
Let:
a = 1, b = \[- \frac{1}{2}\]and c = -4 

Now,

\[\left( 1, - \frac{1}{2} \right) \in R_1 \text{ and }  \left( - \frac{1}{2}, - 4 \right) \in R_1 \] , as 

\[1 + \left( - \frac{1}{2} \right) > 0 \text{ and }  1 + \left( - \frac{1}{2} \right)\left( - 4 \right) > 0\] But 

\[1 + 1 \times \left( - 4 \right) < 0\] 

∴ (1, - 4) \[\not\in R_1\] And,
(a, b) ∈ R₁ and (b , c) ∈ R₁
Thus, (a, c) ∈ R₁ is not true for all a, b, c ∈ R.