Rozwiązanie przedstawiono na rysunku: 

 

Na podstawie powyższego diagramu możemy wyznaczyć zbiory:    

 

$\text{a)}$  

$A\cup B=\left\{1,2,3,4,6,7,8,9\right\}$  

$A\cup C=\left\{1,2,3,4,5,6,9\right\}$  

$A\backslash C=\left\{3,4,9\right\}$  

$B\backslash C=\left\{3,7,8\right\}$  

 

$\text{b)}$  

$A\backslash \left(B\cap C\right)=\left\{3,4,9\right\}$  

$\left(A\backslash B\right)\cap C=\varnothing$  

 

$\text{c)}$  

$A\cup \left(B\cap C\right)=\left\{1,2,3,4,6,9\right\}$  

$\left(A\cup B\right)\cap C=\left\{1,2,6\right\}$  

 

$\text{d)}$  

$A{}^{\prime }=\left\{5,6,7,8,10\right\}$  

$B{}^{\prime }=\left\{4,5,9,10\right\}$  

$C{}^{\prime }=\left\{3,4,7,8,9,10\right\}$  

 

$A{}^{\prime }\cap B{}^{\prime }=\left\{5,10\right\}$  

$A{}^{\prime }\cup C{}^{\prime }=\left\{3,4,5,6,7,8,9,10\right\}$  

$A{}^{\prime }\cup B{}^{\prime }\cup C{}^{\prime }=\left\{3,4,5,6,7,8,9,10\right\}$