Is my understanding about Borel $\sigma$-algebra correct

Question

Regarding the definition of Borel $\sigma$-algebra, let $\Omega=\mathbb{R}$, $\mathcal{O}=\{(a,b):-\infty < a \le b < \infty\}$, can I write Borel $\sigma$-algebra: $\sigma(\mathcal{O})$ as $\sigma(\mathcal{O}) = \{ \varnothing,\mathbb{R},\{(a,b)\},\{(-\infty,a]\},\{[b,+\infty)\}\}$ ?

Thanks and regrads