Is a subset of the real n-dimensional space still in the Borel sigma algebra?

Question

1. If we have a set ${A}\subset{\mathbb{R}^n}$, then is the set ${A}$ a member of the Borel ${\sigma}$-algebra ${\mathcal{B}(\mathbb{R}^n)}$?

2. Suppose ${\mathcal{O}^n}$ is the topology of ${\mathbb{R}^n}$, why ${A}\cap{\mathcal{O}^n}\subset{A}\cap{\sigma(\mathcal{O}^n)}$ holds?

Thanks for help!