Question

Prove
\[if\space A_0\text{ is an algebra, and }A,B \in A_0 \space then \space A\cap B \in A_0 \]

Answer 1

so we know by definition
\[A\in A_0 \implies A^C\in A_0\\and\\A,B \in A_0 \implies A\cup B \in A_0\]

Answer 2

dictionary, duh.

Answer 3

I didn't think this can be complicated to look at http://en.wikipedia.org/wiki/Complement_(set_theory)

Answer 4

de Morgan's\[
A\cup B = (A^C\cap B^C )^C
\]

Answer 5

\[A,B\in A_0\\so\\A^C,B^C\in A_0\\so\\A^C\cup B^C\in A_0\\thus\\(A^C\cup B^C)^C\overset{\large D}{=}\normalsize(A\cap B)\in A_0\]

Answer 6

word I think that works

Answer 7

;) @zzr0ck3r I wish you didn't ask me to delete all my messages

Answer 8

why? I dont need links to wiki telling me what compliment is:)