I want to prove an events boolean algebra property. Is correct?

Question

$C$ has a Boolean algebra structure if and only if:

1. $Ω ∈ C$
2. If $ A ∈ C ⇒ A^c ∈ C$
3. If $A, B ∈ C ⇒ A ∪ B ∈ C$

I want to prove that $0∈C$

1. $Ω ∈ C$
2. If $ Ω ∈ C ⇒ Ω^c ∈ C$

$Ω^c=0 ⇒ 0∈C$

Is correct?

Answer 1

Assuming that $0$ is indeed defined as $\Omega^C$, then yes, that is correct.