TITLE: Example of generated sigma-algebra
QUESTION [5 upvotes]: I looked at the definition of a generated $\sigma$-algebra in wikipedia (https://en.wikipedia.org/wiki/Sigma-algebra) and would like to know if this is correct.
Let $X=\{1,2,3,4\}$ and $F=\{\{1\},\{2\}\}$. Is it correct that $\sigma(F)=\{\emptyset,\{1,2,3,4\},\{1\},\{2,3,4\},\{2\},\{1,3,4\}\}$? Thanks.
edit: The correct answer is $\sigma(F)=\{\emptyset,\{1,2,3,4\},\{1\},\{2,3,4\},\{2\},\{1,3,4\},\{1,2\},\{3,4\}\}$.

REPLY [4 votes]: You missed
$$\{ 3,4 \} = \{ 1,3,4 \} \cap  \{ 2,3,4 \}$$
and
$$\{ 1,2 \} = \{ 1 \} \cup  \{ 2 \}$$
Adding these two, you get a $\sigma$-algebra.