Take \(\mathbb{R}\) to be your reference set, and consider these subsets:

\[ \begin{align*} A&=[1,\,5]\\ B&=\{x\in\mathbb{R}\,:\,|x|>2\}\\ C&=(-\infty,\,0]\\ I_n&=\left[0,\,\frac{1}{n}\right] \end{align*} \]

Express each of the following in as simplified and concise a form as possible:

1. \(A^c\)
2. \(A \cup B\)
3. \(A\cap C\)
4. \(A\cap C^c\)
5. \(B \cap C^c\)
6. \(A^c \cap B^c \cap C^c\)
7. \((A \cup B) \cap C\)
8. \(\bigcap_{n=1}^\infty I_n\)
9. \(\bigcup_{n=1}^\infty I_n\)