$\textbf{Algebra}$
Let $X$ be a set. A collection $\mathscr{A}$ of subsets of $X$ is an algebra on $X$ if
1) $X\in\mathscr{A}$
2) $A\in\mathscr{A}\implies A^\complement\in \mathscr{A}$
3) $A,B\in \mathscr{A}\implies A\cup B\in \mathscr{A}$
Note: It follows from these three conditions that
a) $\varnothing\in \mathscr{A}$
b) $A,B\in\mathscr{A}\implies A\cap B\in \mathscr{A}$
$\textbf{Algebra}$
Let $X$ be a set. A collection $\mathscr{A}$ of subsets of $X$ is an algebra on $X$ if
1) $X\in\mathscr{A}$
2) $A\in\mathscr{A}\implies A^\complement\in \mathscr{A}$
3) $A,B\in \mathscr{A}\implies A\cup B\in \mathscr{A}$
Note: It follows from these three conditions that
a) $\varnothing\in \mathscr{A}$
b) $A,B\in\mathscr{A}\implies A\cap B\in \mathscr{A}$
copied
๐๐ฅ๐ ๐๐๐ซ๐
Let ๐ be a set. A collection ๐ of subsets of ๐ is an algebra on ๐ if
1) ๐โ๐
2) ๐ดโ๐ โน ๐ดแถโ๐
3) ๐ด,๐ตโ๐ โน ๐ดโช๐ตโ๐
Note: It follows from these three conditions that
a) โ โ๐
b) ๐ด,๐ตโ๐ โน ๐ดโฉ๐ตโ๐