zzr0ck3r
  • zzr0ck3r
Prove \[if\space A_0\text{ is an algebra, and }A,B \in A_0 \space then \space A\cap B \in A_0 \]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
zzr0ck3r
  • zzr0ck3r
so we know by definition \[A\in A_0 \implies A^C\in A_0\\and\\A,B \in A_0 \implies A\cup B \in A_0\]
Psymon
  • Psymon
dictionary, duh.
nincompoop
  • nincompoop
I didn't think this can be complicated to look at http://en.wikipedia.org/wiki/Complement_(set_theory)

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anonymous
  • anonymous
de Morgan's\[ A\cup B = (A^C\cap B^C )^C \]
zzr0ck3r
  • zzr0ck3r
\[A,B\in A_0\\so\\A^C,B^C\in A_0\\so\\A^C\cup B^C\in A_0\\thus\\(A^C\cup B^C)^C\overset{\large D}{=}\normalsize(A\cap B)\in A_0\]
zzr0ck3r
  • zzr0ck3r
word I think that works
nincompoop
  • nincompoop
;) @zzr0ck3r I wish you didn't ask me to delete all my messages
zzr0ck3r
  • zzr0ck3r
why? I dont need links to wiki telling me what compliment is:)

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