$X=\left\{x\in \mathbb{N}:0<x<5\right\}=\left\{1,2,3,4\right\}$  

$Y=\left\{x\in \mathbb{N}:0<x\le 3\right\}=\left\{1,2,3\right\}$  

$Z=\left\{x\in \mathbb{N}:4\le x\le 5\right\}=\left\{4,5\right\}$  

Sprawdzamy, który z podanych zbiorów jest równy X. 

$\text{A.}\left(X\cup Z\right)\text{}Y=\left(\left\{1,2,3,4\right\}\cup \left\{1,2,3\right\}\right)\text{}\left\{4,5\right\}=\left\{1,2,3,4\right\}\text{}\left\{4,5\right\}=$  

$=\left\{1,2,3\right\}=Y$  

$\text{B.}X\cap \left(Y\text{}Z\right)=\left\{1,2,3,4\right\}\cap \left(\left\{1,2,3\right\}\text{}\left\{4,5\right\}\right)=\left\{1,2,3,4\right\}\cap \left\{1,2,3\right\}=$  

$=\left\{1,2,3\right\}=Y$  

$\text{C.}Y\cup \left(X\cap Z\right)=\left\{1,2,3\right\}\cup \left(\left\{1,2,3,4\right\}\cap \left\{4,5\right\}\right)=\left\{1,2,3\right\}\cup \left\{4\right\}=$  

$=\left\{1,2,3,4\right\}=X$  

$\text{D.}\left(Z\text{}Y\right)\cup X=\left(\left\{4,5\right\}\text{}\left\{1,2,3\right\}\right)\cup \left\{1,2,3,4\right\}=\left\{4,5\right\}\cup \left\{1,2,3,4\right\}=$  

$=\left\{1,2,3,4,5\right\}$  

Odpowiedź: C