Discrete Mathematics with Applications 4th Edition

$\,\,a.\,\, B_{1}\cup B_{2}\cup B_{3}\cup B_{4}= B_{4}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq 4 \right \}$ $b.\,\, \,\,\,B_{1}\cap B_{2}\cap B_{3}\cap B_{4}= B_{1}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq 1 \right \}$ $c.\,\,B_{1},B_{2},B_{3},B_{4}\,\,are\,\,not\,\,mutually\,\, disjoint$
$B_{i}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq i \right \} for \,\, i =1,2,3,4$ $B_{1}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq 1 \right \}$ $B_{2}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq 2 \right \}$ $B_{3}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq 3 \right \}$ $B_{4}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq 4 \right \}$ $we\,\, notice\,\, that\,\, B_{1}\subseteq B_{2}\subseteq B_{3}\subseteq B_{4}$ $so\,\,a.\,\, B_{1}\cup B_{2}\cup B_{3}\cup B_{4}= B_{4}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq 4 \right \}$ $and\,\, b.\,\, \,\,\,B_{1}\cap B_{2}\cap B_{3}\cap B_{4}= B_{1}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq 1 \right \}$ $B_{1},B_{2},B_{3},B_{4}\,\,are\,\,not\,\,mutually\,\, disjoint\,\,as\,\,for\,example\,$ $B_{2}\cap B_{4}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq 2 \right \}\cap \left \{ x\in \mathbb{R}\mid 0\leq x\leq 4 \right \}=\left \{ x\in \mathbb{R}\mid 0\leq x\leq 2 \right \}\neq \varnothing$