- $ {\\\mathbb{N}^*} \\\cap \\\mathbb{Q} = {\\\mathbb{N}^*}$.
- $ {\\\mathbb{N}^*} \\\cap \\\mathbb{Z} = \\\mathbb{Z}$.
- $ {\\\mathbb{N}^*} \\\cup \\\mathbb{N} = \\\mathbb{Z}$.
- $ \\\mathbb{R}\\\backslash \\\mathbb{Q} = \\\mathbb{N}$.