Answer
$a-(0,\infty)\\
b-(4,\infty)\\
c-no\,\,W_{0},W_{1},W_{2},....are\,not\,\,mutually\,\,disjoint \\
d-(0,\infty)\\
e-(n,\infty)\\
f-(0,\infty)\\
g-\varnothing$
Work Step by Step
$W_{i}=\left \{ x\in \mathbb{R}\mid x> i \right \}\,\,for\,all\,\,nonnegative\,\,integers\,\,i \\
this\,\,mean\,\,that\,\,W_{0}=\left \{ x\in \mathbb{R}\mid x> 0 \right \}\\ W_{1}=\left \{ x\in \mathbb{R}\mid x> 1 \right \}\\
W_{2}=\left \{ x\in \mathbb{R}\mid x> 2 \right \},W_{3}=\left \{ x\in \mathbb{R}\mid x> 3 \right \}\\
W_{4}=\left \{ x\in \mathbb{R}\mid x> 4 \right \}....W_{n}=\left \{ x\in \mathbb{R}\mid x> n \right \}\\
{\color{Red} a-\,\,}\bigcup_{i=0}^{4}W_{i}=W_{0}\cup W_{1}\cup W_{2}\cup W_{3}\cup W_{4}=\left \{ x\in \mathbb{R}\mid x> 0 \right \}\cup \left \{ x\in \mathbb{R}\mid x> 1 \right \}\cup \left \{ x\in \mathbb{R}\mid x> 2 \right \}\cup \left \{ x\in \mathbb{R}\mid x> 3 \right \}\cup \left \{ x\in \mathbb{R}\mid x> 4 \right \}=\left \{ x\in \mathbb{R}\mid x> 0 \right \}=\left ( 0,\infty \right ) \\$
${\color{Red} b-\,\,}\bigcap_{i=0}^{4}W_{i}=W_{0}\cap W_{1}\cap W_{2}\cap W_{3}\cap W_4=\left \{ x\in \mathbb{R}\mid x> 0 \right \}\cap \left \{ x\in \mathbb{R}\mid x> 1 \right \}\cap \left \{ x\in \mathbb{R}\mid x> 2 \right \}\cap \left \{ x\in \mathbb{R}\mid x> 3 \right \}\cap \left \{ x\in \mathbb{R}\mid x> 4 \right \}=\left \{ x\in \mathbb{R}\mid x> 4 \right \}=\left ( 4,\infty \right )$
${\color{Red} c-\,\,}W_{0},W_{1},W_{2},W_{3},W_{4},.....\,\,are\,\,not\,\,mutually\,\,disjoint\,\,as\,\,for\,\,example \\
W_{0}\,\,\cap W_{1}=\left \{ x\in \mathbb{R}\mid x> 0 \right \}\cap \left \{ x\in \mathbb{R}\mid x> 1 \right \}=\left \{ x\in \mathbb{R}\mid x> 1 \right \}=\left ( 1,\infty \right )\neq \varnothing $
${\color{Red} d-\,\,}\bigcup_{i=0}^{n}W_{i}=\left \{ x\in \mathbb{R}\mid x> 0 \right \}\cup \left \{ x\in \mathbb{R}\mid x> 1 \right \}\cup \left \{ x\in \mathbb{R}\mid x> 2 \right \}\cup ...\left \{ x\in \mathbb{R}\mid x> n \right \}=\left \{ x\in \mathbb{R}\mid x> 0 \right \}=\left ( 0,\infty \right ) \\
{\color{Red}e-\,\, }\bigcap_{i=0}^{n}W_{i}=W_{0}\cap W_{1}\cap W_{2}\cap ...W_{n}=\left \{ x\in \mathbb{R}\mid x> 0 \right \}\cap \left \{ x\in \mathbb{R}\mid x> 1 \right \}\cap .....\left \{ x\in \mathbb{R}\mid x> n \right \}=\left ( n,\infty \right )$
${\color{Red} f-\,\,}\bigcup_{i=0}^{\infty }W_{i}=\lim_{n\rightarrow \infty }\bigcup_{i=0}^{n }W_{i}=\left ( 0,\infty \right ) \\
{\color{Red} g-\,\,}\bigcap_{i=0}^{\infty }W_{i}=\lim_{n\rightarrow \infty }\bigcap_{i=0}^{n}W_{i}=\lim_{n\rightarrow \infty }\left ( n,\infty \right )=\varnothing \,\,as\,\,n\,becomes\,\,\,in\! finitel\! y\,\,bigger\,\,(n,\infty)will\,not\,contain\,elements
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