find sigma Algebra of X If the function $X:\mathbb{R}\to\mathbb{R}$ defined by $X:=I_{[0,1]}+4I_{[2,4]}.$ 
What is $\sigma(X)$ 
Could it be
$\{B_1\cup B_2\cup B_3:B_1\subseteq\{[0,1]\},B_2\subseteq\{[2,4]\},
B_3\subseteq \{(-\infty,1)\cup(1,2)\cup(4,\infty)\}\}$ ??

$\sigma (X)$ is same as $\sigma ([0,1],[2,4])$. In general $\sigma (A,B)=\{ \varnothing, \mathbb  R, A,B,A^{c},B^{c}, A\cap B, B\cup A, B^{c}\cap A, B\cap A^{c},B^{c}\cup A, B\cup A^{c}, B^{c}\cup A^{c},B^{c}\cap A^{c}\}$.
