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[tex]N\cup N^{*}=N[/tex]
[tex]N\cap N^{*}=N^{*}[/tex]
[tex]N\setminus N^{*}=(0)[/tex]
[tex]N\cup N_{p}=N[/tex]
[tex]N\cap N_{p}=N_{p}[/tex]
[tex]N\setminus N_{p}=N_{i}[/tex]
[tex]N\cup N_{i}=N[/tex]
[tex]N\cap N_{i}=N_{i}[/tex]
[tex]N\setminus N_{i}=N_{p}[/tex]
[tex]N_{p}\cup N_{i}=N[/tex]
[tex]N_{p}\cap N_{i}=()[/tex]
[tex]N_{p}\setminus N_{i}=N_{p}[/tex]
[tex]N_{i}\setminus N_{p}=N_{i}[/tex]
[tex]N\cup ()=N[/tex]
[tex]N\cap ()=()[/tex]
[tex]N^{*}\cup ()=N^{*}[/tex]
[tex]N^{*}\cap ()=()[/tex]
[tex]N_{i}\cup ()=N_{i}[/tex]
[tex]N_{i}\cap ()=()[/tex]
[tex]N_{p}\cup ()=N_{p}[/tex]
[tex]N_{p}\cap ()=()[/tex]