Understanding why the family of sets is not an algebra Let $\mathcal{F} = \{A \subseteq \Omega: |A| \text{ is even} \}$ be a family of sets of $\Omega$ = $\{1, 2, 3, ..., 2n \}$ for some $n \in \mathbb{N}$ and let $\Omega \in \mathcal{F}$. I am able to show that this family of sets satisfies the following two properties:

*

*Closed under complements

*Closed under finite disjoint unions

However, I want to show that it is not an algebra. Specifically I want to show that it is $\textbf{not}$ closed under finite unions.
I get lost when trying to show that it is not closed under finite unions because I can't think of a case where closed under disjoint unions $\nRightarrow$ closed under unions.
edit:
I should specify that an algebra satisfies the following properties:

*

*$\Omega$ $\in$ $\mathcal{F}$

*Closed under complements

*Closed under finite unions

Thanks for the help.

I assume $n \geq 2$ (if $n=1$, then $\mathcal{F}= \{\emptyset, \{1,2\}\}$ is closed under finite unions).
The union $\{1,2,3\}=\{1,2\}\cup \{2,3\}$ is not in $\mathcal{F}$ so $\mathcal{F}$ is not closed under finite unions.
