[tex]\it a)\ \ x\in\mathbb{N}\\ \\ x<\sqrt{18} \Rightarrow x\leq{16} \Rightarrow x\leq4 \Rightarrow A=\{0,\ \ 1,\ \ 2,\ \ 3,\ \ 4\}\\ \\ \dfrac{6}{x-3}\in\mathbb{N} \Rightarrow x-3\in D_6 \Rightarrow x-3\in\{1,\ 2,\ 3,\ 6\}|_{+3}\Rightarrow B=\{4,\ 5,\ 6,\ 9\}\\ \\ \\ A-B=\{0,\ \ 1,\ \ 2,\ \ 3\}\\ \\ A\cup B=\{0,\ \ 1,\ \ 2,\ \ 3,\ \ 4,\ \ 5,\ \ 6,\ \ 9\}[/tex]
[tex]\it c)\ \ x\in\mathbb{N} \Rightarrow |x|=x\\ \\ |x|<a \Rightarrow x<a \Rightarrow C=\{0,\ 1,\ 2,\ 3,\ 4,\ 5,\ ..,\ (a-1)\}\\ \\ card(B\cap C)=0 \Rightarrow B\cap C=\varnothing \Rightarrow a\in\{ 1,\ \ 2,\ \ 3,\ \ 4\}[/tex]
